Tootfinder

Infinite convex geometries with lower semi-modularity and join semi-distributivity
Adam Mata
https://arxiv.org/abs/2508.15511 https://arxiv.org/pdf/2508.15…

Infinite convex geometries with lower semi-modularity and join semi-distributivity
The following article treats about convex geometries which are lower semi-modular and join semi-distributive lattices. Firstly, it is shown that there is a class $K$ of infinite convex geometries which can be build out of finite ones by using the construction of a union of a chain. Then it is shown that elements of $K$ preserve lower semi-modularity and join semi-distributivity which are not default properties in the infinite setting. It is also discussed that not all of the infinite convex geo…

Exploring the Theory and Practice of Concurrency in the Entity-Component-System Pattern
Patrick Redmond, Jonathan Castello, Jos\'e Manuel Calder\'on Trilla, Lindsey Kuper
https://arxiv.org/abs/2508.15264

Exploring the Theory and Practice of Concurrency in the Entity-Component-System Pattern
The Entity-Component-System (ECS) software design pattern, long used in game development, encourages a clean separation of identity (entities), data properties (components), and computational behaviors (systems). Programs written using the ECS pattern are naturally concurrent, and the pattern offers modularity, flexibility, and performance benefits that have led to a proliferation of ECS frameworks. Nevertheless, the ECS pattern is little-known and not well understood outside of a few domains. …

Socio-Technical Smell Dynamics in Code Samples: A Multivocal Review on Emergence, Evolution, and Co-Occurrence
Arthur Bueno, Bruno Cafeo, Maria Cagnin, Awdren Font\~ao
https://arxiv.org/abs/2507.13481

Socio-Technical Smell Dynamics in Code Samples: A Multivocal Review on Emergence, Evolution, and Co-Occurrence
Code samples play a pivotal role in open-source ecosystems (OSSECO), serving as lightweight artifacts that support knowledge transfer, onboarding, and framework adoption. Despite their instructional relevance, these samples are often governed informally, with minimal review and unclear ownership, which increases their exposure to socio-technical degradation. In this context, the co-occurrence and longitudinal interplay of code smells (e.g., large classes, poor modularity) and community smells (…

Near-Term Quantum-Computing-Inspired Sampling for Community Detection in Low-Modularity Graphs
Joseph Geraci, Luca Pani
https://arxiv.org/abs/2509.03864 https://

Near-Term Quantum-Computing-Inspired Sampling for Community Detection in Low-Modularity Graphs
Low modularity networks (Q < 0.2) challenge classical community detection algorithms, which get trapped in local optima. We introduce quantum inspired community detection algorithms leveraging non classical sampling techniques to escape modularity optimization plateaus. Using distributions inspired by quantum phenomena including Porter Thomas distributions, Haar random states, and hyperuniform point processes, our approach generates diverse high quality partitions that improve modularity on dif…

Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples
Zhineng Cao, Liuquan Wang
https://arxiv.org/abs/2508.12468 https://arxiv.org/pdf/2…

Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples
We find nine new sets of rank four Nahm sums associated with nine different numeric matrices which are likely to be modular. They are discovered by applying the lift-dual operation to some modular rank three Nahm sums in the works of Zagier and the authors. We prove the modularity of four sets of these Nahm sums by establishing Rogers--Ramanujan type identities which express them as modular infinite products. We use various $q$-series techniques including the constant term method and Bailey pai…

$c_\text{eff}$ from Surgery and Modularity
Shimal Harichurn, Mrunmay Jagadale, Dmitry Noshchenko, Davide Passaro
https://arxiv.org/abs/2508.10087 https://a…

$c_\text{eff}$ from Surgery and Modularity
$\widehat{Z}$ invariants, rigorously defined for negative definite plumbed 3-manifolds, are expected--on physical grounds--to exist for every closed, oriented 3-manifold. Several prescriptions have been proposed to extend their definition to generic plumbings by reversing the orientation of a negative definite plumbing, thus turning it into a positive definite one. Two existing proposals are relevant for this paper: (i) the regularized $+1/r$-surgery conjecture combined with the false-mock modu…

Love the modularity of the @… laptops. And real Ethernet l! (Tho does stick out when installed)

Modular SAIL: dream or reality?
Petr Kourzanov, Anmol
https://arxiv.org/abs/2507.12471 https://arxiv.org/pdf/2507.12471

Modular SAIL: dream or reality?
In order to truly benefit from RISC-V ISA modularity, the community has to address the issue of compositionality, going beyond modules at the specification level covering larger subsets of the RISC-V development flow including emulation, simulation and verification. In this paper we introduce modular SAIL, an experiment to inject compositionality into the SAIL-RISCV golden model. We show that it is, in principle, not difficult to adapt the SAIL-RISCV flow (and ideally the SAIL compiler itself) …

MESA-QUEST: Modeling Quasi-Stars in MESA
Claire B. Campbell, Andrew D. Santarelli, Matthew E. Caplan
https://arxiv.org/abs/2507.12651 https://

MESA-QUEST: Modeling Quasi-Stars in MESA
Supermassive black hole formation remains an unsolved problem. Quasi-stars have been suggested as a viable heavy-seeding mechanism. In this work, we implement methods for modeling quasi-stars previously used with the Cambridge STARS code into the 1D stellar evolution code MESA. The computational capabilities of MESA allow for more detailed simulations of quasi-star evolution due to its modularity and the ease of implementing of new physical processes and controls. Our implementation, the MESA Q…

Crosslisted article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- $c_\text{eff}$ from Surgery and Modularity
Shimal Harichurn, Mrunmay Jagadale, Dmitry Noshchenko, Davide Passaro

No Community Detection Method to Rule Them All!
Shrabani Ghosh, Erik Saule
https://arxiv.org/abs/2509.11490 https://arxiv.org/pdf/2509.11490

No Community Detection Method to Rule Them All!
Community detection is a core tool for analyzing large realworld graphs. It is often used to derive additional local features of vertices and edges that will be used to perform a downstream task, yet the impact of community detection on downstream tasks is poorly understood. Prior work largely evaluates community detection algorithms by their intrinsic objectives (e.g., modularity). Or they evaluate the impact of using community detection onto on the downstream task. But the impact of particula…

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- $c_\text{eff}$ from Surgery and Modularity
Shimal Harichurn, Mrunmay Jagadale, Dmitry Noshchenko, Davide Passaro

Too Helpful, Too Harmless, Too Honest or Just Right?
Gautam Siddharth Kashyap, Mark Dras, Usman Naseem
https://arxiv.org/abs/2509.08486 https://arxiv.org/p…

Too Helpful, Too Harmless, Too Honest or Just Right?
Large Language Models (LLMs) exhibit strong performance across a wide range of NLP tasks, yet aligning their outputs with the principles of Helpfulness, Harmlessness, and Honesty (HHH) remains a persistent challenge. Existing methods often optimize for individual alignment dimensions in isolation, leading to trade-offs and inconsistent behavior. While Mixture-of-Experts (MoE) architectures offer modularity, they suffer from poorly calibrated routing, limiting their effectiveness in alignment ta…

Fairphone announces the €599 Fairphone 6, with a 6.31" 120Hz LTPO OLED display, a Snapdragon 7s Gen 3 chip, and enhanced modularity with 12 swappable parts (Andrew Liszewski/The Verge)
https://www.theverge.com/news/692248/fairp

The smaller Fairphone 6 introduces swappable accessories
The Fairphone 6 is smaller and lighter but offers better battery life and a more modular design, making it easier to repair and upgrade than other phones.

On Some Hypergeometric Modularity Conjectures of Dawsey and McCarthy
Brian Grove
https://arxiv.org/abs/2507.19971 https://arxiv.org/pdf/2507.19971

On Some Hypergeometric Modularity Conjectures of Dawsey and McCarthy
In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large class of hypergeometric Galois representations in dimensions two and three. One important application of the EHMM is the construction of an explicit family of eta-quotients, which we call the $\mathbb{K}_{2}$ functions, from the hypergeometric background. In this article, we introduce an analogous family of eta-quotien…

Programmable Locking Cells (PLC) for Modular Robots with High Stiffness Tunability and Morphological Adaptability
Jianshu Zhou, Wei Chen, Junda Huang, Boyuan Liang, Yunhui Liu, Masayoshi Tomizuka
https://arxiv.org/abs/2509.07916

Programmable Locking Cells (PLC) for Modular Robots with High Stiffness Tunability and Morphological Adaptability
Robotic systems operating in unstructured environments require the ability to switch between compliant and rigid states to perform diverse tasks such as adaptive grasping, high-force manipulation, shape holding, and navigation in constrained spaces, among others. However, many existing variable stiffness solutions rely on complex actuation schemes, continuous input power, or monolithic designs, limiting their modularity and scalability. This paper presents the Programmable Locking Cell (PLC)-a …

Characterization of the near-null error components utilized in composite adaptive AMG solvers
Austen J. Nelson, Panayot S. Vassilevski
https://arxiv.org/abs/2509.09023 https://

Characterization of the near-null error components utilized in composite adaptive AMG solvers
We provide a theoretical justification for the construction of adaptive composite solvers based on a sequence of AMG (algebraic multigrid) $μ$-cycle methods that exploit error components that the current solver cannot damp efficiently. Each solver component is an aggregation based AMG where its aggregates are constructed using the popular in graph community detection modularity matrix. The latter utilizes the given matrix and the error component vector the current solver cannot handle. The per…

NeedForHeat DataGear: An Open Monitoring System to Accelerate the Residential Heating Transition
Henri ter Hofte, Nick van Ravenzwaaij
https://arxiv.org/abs/2509.06927 https://

NeedForHeat DataGear: An Open Monitoring System to Accelerate the Residential Heating Transition
We introduce NeedForHeat DataGear: an open hardware and open software data collection system designed to accelerate the residential heating transition. NeedForHeat DataGear collects time series monitoring data in homes that have not yet undergone a heating transition, enabling assessment of real-life thermal characteristics, heating system efficiency, and residents' comfort needs. This paper outlines its architecture and functionalities, emphasizing its modularity, adaptability, and cost-effect…

LL3M: Large Language 3D Modelers
Sining Lu, Guan Chen, Nam Anh Dinh, Itai Lang, Ari Holtzman, Rana Hanocka
https://arxiv.org/abs/2508.08228 https://arxiv.o…

LL3M: Large Language 3D Modelers
We present LL3M, a multi-agent system that leverages pretrained large language models (LLMs) to generate 3D assets by writing interpretable Python code in Blender. We break away from the typical generative approach that learns from a collection of 3D data. Instead, we reformulate shape generation as a code-writing task, enabling greater modularity, editability, and integration with artist workflows. Given a text prompt, LL3M coordinates a team of specialized LLM agents to plan, retrieve, write,…

Holographic thermal propagator from modularity
Borut Bajc, Katarina Trailovi\'c
https://arxiv.org/abs/2509.02226 https://arxiv.org/pdf/2509.02226

Holographic thermal propagator from modularity
It is known that the holographic thermal propagator in 4 spacetime dimensions can be related to the Nekrasov-Shatashvili limit of the $Ω$-deformed ${\cal N}=2$ supersymmetric $SU(2)$ Yang-Mills theory with $N_f=4$ hypermultiplets. There are two expansions involved: one is the expansion in small temperature which in the Seiberg-Witten language is equivalent to the semiclassical expansion in inverse powers of the large adjoint vev and the second is the expansion in instanton numbers. Working in …

Compositional Control-Driven Boolean Circuits
Damian Arellanes
https://arxiv.org/abs/2506.22687 https://arxiv.org/pdf/2506.22687

Compositional Control-Driven Boolean Circuits
Boolean circuits abstract away from physical details to focus on the logical structure and computational behaviour of digital components. Despite they have been studied for many decades, compositionality has been widely ignored or examined in an informal manner, which is a property for combining circuits without delving into their internal structure, while supporting modularity and formal reasoning. In this paper, we address this longstanding theoretical gap by proposing colimit-based operators…

Composable Effect Handling for Programming LLM-integrated Scripts
Di Wang
https://arxiv.org/abs/2507.22048 https://arxiv.org/pdf/2507.22048

Composable Effect Handling for Programming LLM-integrated Scripts
Implementing LLM-integrated scripts introduces challenges in modularity and performance, as scripts are often coupled to specific LLM implementations and fail to exploit parallelization opportunities. This paper proposes using composable effect handling to separate workflow logic from effectful operations, such as LLM calls, I/O, and concurrency, enabling modularity without sacrificing the opportunity for performance optimization. By treating these operations as abstract interfaces and discharg…

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
Yuya Murakami
https://arxiv.org/abs/2508.21710 https://

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing quantum modularity of false theta functions. Previous progress covers Seifert homology 3-spheres for the former and rank-one cases for the latter, both of which rely on single-variable integral representations. We extend these results to negative definite plumbed 3-manifolds and to general false theta…

Grid-Forming Vector Current Control FRT Modes Under Symmetrical and Asymmetrical Faults
Ognjen Stanojev, Orcun Karaca, Mario Schweizer
https://arxiv.org/abs/2508.03389 https://

Grid-Forming Vector Current Control FRT Modes Under Symmetrical and Asymmetrical Faults
Recent research has shown that operating grid-connected converters using the grid-forming vector current control (GFVCC) scheme offers significant benefits, including the simplicity and modularity of the control architecture, as well as enabling a seamless transition from PLL-based grid-following control to grid-forming. An important aspect of any grid-connected converter control strategy is the handling of grid-fault scenarios such as symmetrical and asymmetrical short-circuit faults. This pap…

Replaced article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- Mock Modularity Of Twisted Index In CHL Models
Nabamita Banerjee, Vedant Bhutra, Ranveer Kumar Singh
…

pyFAST: A Modular PyTorch Framework for Time Series Modeling with Multi-source and Sparse Data
Zhijin Wang, Senzhen Wu, Yue Hu, Xiufeng Liu
https://arxiv.org/abs/2508.18891 http…

pyFAST: A Modular PyTorch Framework for Time Series Modeling with Multi-source and Sparse Data
Modern time series analysis demands frameworks that are flexible, efficient, and extensible. However, many existing Python libraries exhibit limitations in modularity and in their native support for irregular, multi-source, or sparse data. We introduce pyFAST, a research-oriented PyTorch framework that explicitly decouples data processing from model computation, fostering a cleaner separation of concerns and facilitating rapid experimentation. Its data engine is engineered for complex scenarios…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Infinite convex geometries with lower semi-modularity and join semi-distributivity
Adam Mata

Post-estimation Adjustments in Data-driven Decision-making with Applications in Pricing
Michael Albert, Max Biggs, Ningyuan Chen, Guan Wang
https://arxiv.org/abs/2507.20501 http…

Post-estimation Adjustments in Data-driven Decision-making with Applications in Pricing
The predict-then-optimize (PTO) framework is a standard approach in data-driven decision-making, where a decision-maker first estimates an unknown parameter from historical data and then uses this estimate to solve an optimization problem. While widely used for its simplicity and modularity, PTO can lead to suboptimal decisions because the estimation step does not account for the structure of the downstream optimization problem. We study a class of problems where the objective function, evaluat…

An Open-Sourced, Community-Driven Volumetric Additive Manufacturing Printer and Post-Processor
Taylor Waddell, Erik Broude, Tristan Bourgade, Natalia Fabiana De La Torre, Erfan Kohyarnejadfard, Tavleen Kaur, Scarlett Hao, Dylan Motley, Daniel Oslund, Evan Percival, Connor Vidmar, Hayden Taylor
https://arxiv.org/abs/2509.02865

An Open-Sourced, Community-Driven Volumetric Additive Manufacturing Printer and Post-Processor
OpenCAL is a low cost CAL based printing and post processing platform developed using commercial off the shelf (COTS) components and standard rapid prototyping tools. The system incorporates recent advancements in VAM, including Optical Scattering Tomography (OST), and is designed with modularity to support future technological integration. The post processing systems developed include standardized procedures for solvent based removal of uncured resin and a centrifugal cleaning module for enhan…

Crosslisted article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- $c_\text{eff}$ from Surgery and Modularity
Shimal Harichurn, Mrunmay Jagadale, Dmitry Noshchenko, Davide Passaro

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Origami: real structure, enumeration and quantum modularity
Rapha\"el Fesler, Peter Zograf

Mapple: A Domain-Specific Language for Mapping Distributed Heterogeneous Parallel Programs
Anjiang Wei, Rohan Yadav, Hang Song, Wonchan Lee, Ke Wang, Alex Aiken
https://arxiv.org/abs/2507.17087

Mapple: A Domain-Specific Language for Mapping Distributed Heterogeneous Parallel Programs
Optimizing parallel programs for distributed heterogeneous systems remains a complex task, often requiring significant code modifications. Task-based programming systems improve modularity by separating performance decisions from core application logic, but their mapping interfaces are often too low-level. In this work, we introduce Mapple, a high-level, declarative programming interface for mapping distributed applications. Mapple provides transformation primitives to resolve dimensionality mi…

Dense Subgraph Clustering and a New Cluster Ensemble Method
The-Anh Vu-Le, Jo\~ao Alfredo Cardoso Lamy, Tom\'as Alessi, Ian Chen, Minhyuk Park, Elfarouk Harb, George Chacko, Tandy Warnow
https://arxiv.org/abs/2508.17013

Dense Subgraph Clustering and a New Cluster Ensemble Method
We propose DSC-Flow-Iter, a new community detection algorithm that is based on iterative extraction of dense subgraphs. Although DSC-Flow-Iter leaves many nodes unclustered, it is competitive with leading methods and has high-precision and low-recall, making it complementary to modularity-based methods that typically have high recall but lower precision. Based on this observation, we introduce a novel cluster ensemble technique that combines DSC-Flow-Iter with modularity-based clustering, to pr…

Recourse, Repair, Reparation, & Prevention: A Stakeholder Analysis of AI Supply Chains
Aspen K. Hopkins, Isabella Struckman, Kevin Klyman, Susan S. Silbey
https://arxiv.org/abs/2507.02648

Recourse, Repair, Reparation, & Prevention: A Stakeholder Analysis of AI Supply Chains
The AI industry is exploding in popularity, with increasing attention to potential harms and unwanted consequences. In the current digital ecosystem, AI deployments are often the product of AI supply chains (AISC): networks of outsourced models, data, and tooling through which multiple entities contribute to AI development and distribution. AI supply chains lack the modularity, redundancies, or conventional supply chain practices that enable identification, isolation, and easy correction of fai…

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
Conghuan Luo, Yifan Wang

Quantum invariants of 3-manifolds and links: a review
John Chae
https://arxiv.org/abs/2509.02939 https://arxiv.org/pdf/2509.02939

Quantum invariants of 3-manifolds and links: a review
We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity, infinite dimensional Verma module structures and knot-quiver correspondence. Furthermore, they have connections to other topological invariants. We also provide a review of an extension of the above series invariants to Lie superalgebras.

Efficient and scalable inter-module switching for distributed quantum computing architectures
Kamil Bradler
https://arxiv.org/abs/2508.19088 https://arxiv.…

Efficient and scalable inter-module switching for distributed quantum computing architectures
Large-scale fault-tolerant quantum computers of the future will likely be modular by necessity or by design. Modularity is inevitable if the substrate cannot support the desired error-correction code due to its planar geometry or manufacturing constraints resulting in a limited number of logical qubits per module. Even if the computer is compact enough there may be functional requirements to distribute the quantum computation substrate over distant regions of varying scales. In both cases, matt…

LLM-Assisted Semantic Alignment and Integration in Collaborative Model-Based Systems Engineering Using SysML v2
Zirui Li, Stephan Husung, Haoze Wang
https://arxiv.org/abs/2508.16181

LLM-Assisted Semantic Alignment and Integration in Collaborative Model-Based Systems Engineering Using SysML v2
Cross-organizational collaboration in Model-Based Systems Engineering (MBSE) faces many challenges in achieving semantic alignment across independently developed system models. SysML v2 introduces enhanced structural modularity and formal semantics, offering a stronger foundation for interoperable modeling. Meanwhile, GPT-based Large Language Models (LLMs) provide new capabilities for assisting model understanding and integration. This paper proposes a structured, prompt-driven approach for LLM…

CodeDiffuser: Attention-Enhanced Diffusion Policy via VLM-Generated Code for Instruction Ambiguity
Guang Yin, Yitong Li, Yixuan Wang, Dale McConachie, Paarth Shah, Kunimatsu Hashimoto, Huan Zhang, Katherine Liu, Yunzhu Li
https://arxiv.org/abs/2506.16652

CodeDiffuser: Attention-Enhanced Diffusion Policy via VLM-Generated Code for Instruction Ambiguity
Natural language instructions for robotic manipulation tasks often exhibit ambiguity and vagueness. For instance, the instruction "Hang a mug on the mug tree" may involve multiple valid actions if there are several mugs and branches to choose from. Existing language-conditioned policies typically rely on end-to-end models that jointly handle high-level semantic understanding and low-level action generation, which can result in suboptimal performance due to their lack of modularity and interpret…

Proofs of Two Conjectural Identities on Partial Nahm Sums
Changsong Shi, Liuquan Wang
https://arxiv.org/abs/2507.20270 https://arxiv.org/pdf/2507.20270

Proofs of Two Conjectural Identities on Partial Nahm Sums
Recently, Wang and Zeng investigated modularity of partial Nahm sums and discovered 14 modular families of such sums. They confirmed modularity for 13 families and proposed a conjecture consisting of two Rogers--Ramanujan type identities for the remaining family. We prove these conjectural identities in two steps. First, employing a transformation formula involving two Bailey pairs, we transform the partial Nahm sums into some specific Hecke-type series. Second, using two distinct approaches, w…

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Origami: real structure, enumeration and quantum modularity
Rapha\"el Fesler, Peter Zograf

Replaced article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- Modularity of admissible-level $\mathfrak{sl}_{3}$ minimal models with denominator $2$
Justine Fasquel, Christopher Raymond, David Ridout

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Modularity of certain mod $p^n$ Galois representations
Rajender Adibhatla
http…

What is digital about abstraction?
Bernhard Rieder
https://arxiv.org/abs/2508.18181 https://arxiv.org/pdf/2508.18181

What is digital about abstraction?
This chapter examines abstraction as a central principle of computing, not merely as a cognitive skill or epistemological category, but as a material and organizational practice that structures how software is built, used, and embedded in society. By tracing abstraction through historical developments in programming, operating systems, and networking, the text highlights its dual role in enabling modularity and layering while simultaneously shaping cultural, economic, and organizational forms. …

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[2/3]:
- Mock modularity at work, or black holes in a forest
Sergei Alexandrov

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Higher modularity of elliptic curves over function fields
Adam Logan, Jared Weinstein

On a Divisor Modular Form and a Theta Lift
Andreas Mono, Larry Rolen, Johann Stumpenhusen
https://arxiv.org/abs/2509.01378 https://arxiv.org/pdf/2509.01378…

On a Divisor Modular Form and a Theta Lift
In 1975, Zagier introduced the highly influential hyperbolic Poincaré series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $ω_{k+1,D}$. Furthermore, we show that the generating function of $ω_{k+1,D}$ has the same modularity properties as Kohnen and Zagier's fruitful theta kernel generating the $f_{k,D}$'s. This yields a new theta lift.

On the Minimality of the Conductor in Rank Bounds for Elliptic Curves
K. Lakshmanan
https://arxiv.org/abs/2506.20175 https://arxiv.or…

On the Minimality of the Conductor in Rank Bounds for Elliptic Curves
We show that no arithmetic invariant strictly smaller than the conductor of an elliptic curve over \( \mathbb{Q} \) can appear in a functional equation governing the analytic continuation of an associated \( L \)-function of degree two. In particular, any attempt to define a modified \( L \)-function for an elliptic curve with a smaller invariant in place of the conductor leads to a contradiction with the Modularity Theorem. As a consequence, the classical upper bound \( \operatorname{rank}(E) …

An elementary proof of Newman's eta-quotient theorem
David Savitt
https://arxiv.org/abs/2507.16225 https://arxiv.org/pdf/2507.162…

An elementary proof of Newman's eta-quotient theorem
Let eta(z) be the Dedekind eta function. Newman studied the modularity of eta-quotients, giving necessary and sufficient conditions for a function of the form \prod_{0 < m | N} eta(mz)^{r_m} to be a (weakly) holomorphic modular form of level N. We explain a proof of Newman's theorem, developed while teaching a class for talented high school students at Canada/USA Mathcamp. The key observation is that although Gamma_1(N) is not generated by its upper triangular and lower triangular subgroup…