Averages of long Dirichlet polynomials with modular coefficients

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-08-09 DOI:10.1112/mtk.12220

Brian Conrey, Alessandro Fazzari

引用次数: 3

Abstract

We study the moments of L-functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of a long Dirichlet polynomial with modular coefficients. This result, which is conditional on the Generalized Lindelöf Hypothesis, agrees with the prediction of the recipe by Conrey, Farmer, Keating, Rubinstein and Snaith.

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带模系数的长狄利克雷多项式的平均值

我们在权值方面研究了与原始尖形相关的L -函数的矩。特别地，我们得到了具有模系数的长狄利克雷多项式的扭矩的渐近公式。这一结果与Conrey、Farmer、Keating、Rubinstein和Snaith对配方的预测一致，该结果以广义Lindelöf假设为条件。

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

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.