Tootfinder

Generalized splitting of algebras with application to a bialgebra structure of Leibniz algebras induced from averaging Lie bialgebras
Chengming Bai, Li Guo, Guilai Liu, Quan Zhao
https://arxiv.org/abs/2509.14137

Generalized splitting of algebras with application to a bialgebra structure of Leibniz algebras induced from averaging Lie bialgebras
The classical notion of splitting a binary quadratic operad $\mathcal{P}$ gives the notion of pre-$\mathcal{P}$-algebras characterized by $\mathcal{O}$-operators, with pre-Lie algebras as a well-known example. Pre-$\mathcal{P}$-algebras give a refinement of the structure of $\mathcal{P}$-algebras and is critical in the Manin triple approach to bialgebras for $\mathcal{P}$-algebras. Motivated by the new types of splitting appeared in recent studies, this paper aims to extend the classical notion…

Large values of quadratic Dirichlet $L$-functions near the central point
Zikang Dong, Zhonghua Li, Yutong Song, Shengbo Zhao
https://arxiv.org/abs/2508.12205 https://

Large values of quadratic Dirichlet $L$-functions near the central point
In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$-functions near the central point $s=1/2$. When $σ$ closes to $1/2$ within a suitable range, we show that $L(σ, χ_d)$ have the conditional large values of the similar order of magnitude as $L(1/2, χ_d)$.

Estimation in linear models with clustered data
Anna Mikusheva, Mikkel S{\o}lvsten, Baiyun Jing
https://arxiv.org/abs/2508.12860 https://arxiv.org/pdf/2508…

Estimation in linear models with clustered data
We study linear regression models with clustered data, high-dimensional controls, and a complicated structure of exclusion restrictions. We propose a correctly centered internal IV estimator that accommodates a variety of exclusion restrictions and permits within-cluster dependence. The estimator has a simple leave-out interpretation and remains computationally tractable. We derive a central limit theorem for its quadratic form and propose a robust variance estimator. We also develop inference …

Solving Fermat-type equations over quadratic fields
Begum Gulsah Cakti
https://arxiv.org/abs/2509.14280 https://arxiv.org/pdf/2509.14280

Solving Fermat-type equations over quadratic fields
This paper applies the modular approach to obtain effectively computable bounds for Fermat-type equations over number fields, while also discussing the differences and obstructions that arise when considering such equations over totally real versus totally complex number fields. We use these techniques to study the generalized Fermat equation $d^ra^p+b^p+c^p=0$ over quadratic fields $\mathbb{Q}(\sqrt{d})$ of class number one. Extending the results of Freitas\&Siksek and Turcas, we show that whe…

$S$-units and period length of continued fractions of linear recursions
Veekesh Kumar, Vivek Singh, Johannes Sprang
https://arxiv.org/abs/2509.14599 https://

$S$-units and period length of continued fractions of linear recursions
Let $(A_n)_{n\in \mathbb{Z}}$ be a linear recurrence sequence with values in a real quadratic field. In this paper, we study the question whether the period length of the continued fraction of $A_n$ is bounded as $n$ varies. The case where $(A_n)_n$ is a linear recurrence of degree $1$ has previously been solved by Corvaja and Zannier. Their result settled a problem posed by Mendès France about the length of the periods of the continued fractions for $α^n$.

Theory of non-resonant Raman scattering from electrons in nodal and flat bands
Predrag Nikoli\'c
https://arxiv.org/abs/2510.08690 https://arxiv.org/pdf…

Theory of non-resonant Raman scattering from electrons in nodal and flat bands
Raman scattering is emerging as a surprising probe of electron topology in quantum materials. It has been used recently to detect and characterize a topological phase transition that accompanies the magnetic transition in Nd$_2$Ir$_2$O$_7$. Here we present a theory of Raman scattering from nodal electrons with Weyl and quadratic band touching spectra, which has to reach beyond the standard effective mass approximation. After reviewing and providing the details of our previous theory development…

Linearizations of Quadratic Two-parameter Matrix Polynomial Via Newton basis
Avisek Bist, Namita Behera
https://arxiv.org/abs/2509.10470 https://arxiv.org/…

Linearizations of Quadratic Two-parameter Matrix Polynomial Via Newton basis
Given a quadratic two-parameter matrix polynomial in Newton basis $Q_{N} (λ,μ)$, we construct a vector space of linear two-parameter matrix polynomials and identify a set of linearizations which lie in the vector space. We also describe construction of each of these linearizations.

An Explicit Cohen-Style Threefield Identity
Lucas Perryman-Deskins
https://arxiv.org/abs/2508.12152 https://arxiv.org/pdf/2508.12152

An Explicit Cohen-Style Threefield Identity
In 1988, Andrews, Dyson, and Hickerson showed that a $q$-series $σ$ found in Ramanujan's lost notebook and related to partitions could be interpreted as counting ideals in $\mathbb{Q}(\sqrt{6})$, and found similar formulas for $σ$ in terms of ideals of $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(\sqrt{3})$. Cohen followed this by showing more generally that for certain triples of quadratic fields, there is abelian extension and conductor so that the ray class character theta series for all three f…

Improvement of Drmota-Verwee's effective Erdos-Wintner theorem for Zeckendorf expansions
Johann Verwee
https://arxiv.org/abs/2509.14974 https://arxiv.o…

Improvement of Drmota-Verwee's effective Erdos-Wintner theorem for Zeckendorf expansions
We revisit the effective Erdos-Wintner theorem for Zeckendorf expansions. Drmota and the author obtained a uniform Kolmogorov bound whose error involves $T\sum_{j>L-2h}|f(F_j)|$, which assumes absolute convergence of the linear tail $\sum_j f(F_j)$. We remove this assumption. Grouping the transfer matrices in pairs and working to second order on the logarithm of the product, after extracting the common linear phase along the dominant direction, yields a quadratic tail $T^2\sum_{j>L-2h…

Class numbers of Imaginary bicyclic biquadratic number fields
Anuj Jakhar, Ravi Kalwaniya, Mahesh Kumar Ram
https://arxiv.org/abs/2509.13153 https://arxiv.…

Class numbers of Imaginary bicyclic biquadratic number fields
For any fixed positive integer $n$, we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$, along with their class group structures, using the list of all imaginary quadratic number fields whose class numbers divide $2n$. We apply this method to list all imaginary bicyclic biquadratic number fields with class numbers $4$, $6$ and $7$. We also present the class group structure of each subfield of these fields.