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Siegel Zeros of Triple Product L-functions
Shifan Zhao
https://arxiv.org/abs/2508.06423 https://arxiv.org/pdf/2508.06423

Siegel Zeros of Triple Product L-functions
Let $F$ be a number field. Let $π_1,π_2$ be unitary cuspidal automorphic representations of $GL_2(\mathbb{A}_F)$, and let $π$ be a unitary cuspidal automorphic representation of either $GL_2(\mathbb{A}_F)$ or $GL_3(\mathbb{A}_F)$. When $(π_1,π_2,π)$ is of general type, we show that the triple product $L$-function $L(s,π_1 \times π_2 \times π)$ on either $GL(2) \times GL(2) \times GL(2)$ or $GL(2) \times GL(2) \times GL(3)$ has no Siegel zero. Moreover, when $(π_1,π_2,π)$ is not of g…

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Quenching, Fast and Slow: Breaking Kibble-Zurek Universal Scaling by Jumping along Geodesics
Thi Ha Kyaw, Guillermo Romero, Gaurav Saxena
https://arxiv.org/abs/2510.08528 https:…

Quenching, Fast and Slow: Breaking Kibble-Zurek Universal Scaling by Jumping along Geodesics
A major drawback of adiabatic quantum computing (AQC) is fulfilling the energy gap constraint, which requires the total evolution time to scale inversely with the square of the minimum energy gap. Failure to satisfy this condition violates the adiabatic approximation, potentially undermining computational accuracy. Recently, several approaches have been proposed to circumvent this constraint. One promising approach is to use the family of adiabatic shortcut procedures to fast-forward AQC. One c…

Zero-Inflated Bayesian Multi-Study Infinite Non-Negative Matrix Factorization
Blake Hansen, Dafne Zorzetto, Valeria Edefonti, Roberta De Vito
https://arxiv.org/abs/2510.07518 ht…

Zero-Inflated Bayesian Multi-Study Infinite Non-Negative Matrix Factorization
Understanding the association between dietary patterns and health outcomes, such as the cancer risk, is crucial to inform public health guidelines and shaping future dietary interventions. However, dietary intake data present several statistical challenges: they are high-dimensional, often sparse with excess zeros, and exhibit heterogeneity driven by individual-level covariates. Non-Negative Matrix Factorization (NMF), commonly used to estimate patterns in high-dimensional count data, typically…

Robustness of Covariance Estimators with Application in Activity Detection
Hendrik Bernd Zarucha, Peter Jung, Giuseppe Caire
https://arxiv.org/abs/2510.07044 https://

Robustness of Covariance Estimators with Application in Activity Detection
The first part of this work considers a general class of covariance estimators. Each estimator of that class is generated by a real-valued function $g$ and a set of model covariance matrices $H$. If $\bf{W}$ is a potentially perturbed observation of a searched covariance matrix, then the estimator is the minimizer of the sum of $g$ applied to each eigenvalue of $\bf{W}^\frac{1}{2}\bf{Z}^{-1}\bf{W}^\frac{1}{2}$ under the constraint that $\bf{Z}$ is from $H$. It is shown that under mild condition…

Accelerating Sparse Ternary GEMM for Quantized LLM inference on Apple Silicon
Baraq Lipshitz (ETH Zurich), Alessio Melone (ETH Zurich), Charalampos Maraziaris (ETH Zurich), Muhammed Bilal (ETH Zurich)
https://arxiv.org/abs/2510.06957

Accelerating Sparse Ternary GEMM for Quantized LLM inference on Apple Silicon
Sparse Ternary General Matrix-Matrix Multiplication (GEMM) remains under-optimized in existing libraries for Apple Silicon CPUs. We present a Sparse Ternary GEMM kernel optimized specifically for Apple's M-series processors. We propose a set of architecture-aware optimizations, including a novel blocked and interleaved sparse data format to improve memory locality, strategies to increase Instruction-Level Parallelism (ILP), and NEON-based Single Instruction Multiple Data (SIMD) vectorization to…

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Complex moments of the derivative of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
https://arxiv.org/abs/2509.07788 https://arxiv.org/p…

Complex moments of the derivative of the Riemann zeta function
We conjecture results about the complex moments of the derivative of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this via two different random matrix computations. In the first, we find an exact formula for the complex moments of the derivative of the characteristic polynomials of unitary matrices averaged over Haar measure using Selberg's integral. In the second, we consider the hybrid approach for zeta, first proposed by Gonek, Hughes and …

Triadic Fusion of Cognitive, Functional, and Causal Dimensions for Explainable LLMs: The TAXAL Framework
David Herrera-Poyatos, Carlos Pel\'aez-Gonz\'alez, Cristina Zuheros, Virilo Tejedor, Rosana Montes, Francisco Herrera
https://arxiv.org/abs/2509.05199

Triadic Fusion of Cognitive, Functional, and Causal Dimensions for Explainable LLMs: The TAXAL Framework
Large Language Models (LLMs) are increasingly being deployed in high-risk domains where opacity, bias, and instability undermine trust and accountability. Traditional explainability methods, focused on surface outputs, do not capture the reasoning pathways, planning logic, and systemic impacts of agentic LLMs. We introduce TAXAL (Triadic Alignment for eXplainability in Agentic LLMs), a triadic fusion framework that unites three complementary dimensions: cognitive (user understanding), functio…

On Hardy's $Z$-function and its derivatives associated with Selberg class
Hirotaka Kobayashi
https://arxiv.org/abs/2509.06248 https://arxiv.org/pdf/250…

On Hardy's $Z$-function and its derivatives associated with Selberg class
Hardy's $Z$-function $Z(t)$ is a real-valued function of the real valuable $t$, and its zeros exactly correspond to those of the Riemann zeta-function on the critical line. In 2012, K.~Matsuoka showed that for any non-negative integer $k$, there exists a $T=T(k)>0$ such that $Z^{(k+1)}(t)$ has exactly one zero between consecutive zeros of $Z^{(k)}(t)$ for $t\ge T$ under the Riemann Hypothesis. In this article, we extend Matsuoka's theorem to some $L$-functions in Selberg class.