爱森斯坦级数的第一个负傅立叶系数的新形式

IF 0.6 3区数学 Q3 MATHEMATICS

Ramanujan Journal Pub Date : 2023-09-11 DOI:10.1007/s11139-023-00779-1

Sebastián Carrillo Santana

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引用次数: 0

摘要

关于新形式傅里叶系数的符号变化的统计问题，已经有许多论文。在一篇这样的论文中，Linowitz和Thompson给出了一个猜想，描述了爱森斯坦级数新形式的傅里叶系数的第一个负号平均何时出现。本文对他们的猜想进行了修正，并对修正后的版本进行了证明。

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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The first negative Fourier coefficient of an Eisenstein series newform

Abstract There have been a number of papers on statistical questions concerning the sign changes of Fourier coefficients of newforms. In one such paper, Linowitz and Thompson gave a conjecture describing when, on average, the first negative sign of the Fourier coefficients of an Eisenstein series newform occurs. In this paper, we correct their conjecture and prove the corrected version.

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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

期刊介绍： The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections. The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest: Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.