Low-Lying Zeros of L-functions of Adélic Hilbert Modular Forms and their Convolutions

2024/12/04 by Alia Hamieh, Hamieh, Alia, Peng‐Jie Wong +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2412.03034

openalex publication_date 2024/12/04 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28

Abstract

In this article, we study the density conjecture of Katz and Sarnak for L-functions of adélic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances supporting the conjecture and extending the works of Iwaniec-Luo-Sarnak and many others. For applications, we obtain an upper bound for the average order of L-functions of Hilbert modular forms at s=(1)/(2) as well as a positive proportion of non-vanishing of certain Rankin-Selberg L-functions.

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