Riemann hypothesis for period polynomials for cusp forms on Γ0(N)

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-05-30 DOI:10.1142/s1793042124500982

SoYoung Choi

引用次数: 0

Abstract

We prove that for even integer $k$ , almost all of zeros of the period polynomial associated to a cusp form of weight $k$ on $Γ_{0} (N)$ are on the circle $| z | = 1 / \sqrt{N}$ under some conditions.

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Γ0(N)上尖顶形式周期多项式的黎曼假设

我们证明，对于偶数整数 k，在某些条件下，Γ0(N) 上与权重为 k 的尖顶形式相关的周期多项式的几乎所有零点都位于圆 |z|=1/N 上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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