Ratios conjecture for quadratic Hecke L-functions in the Gaussian field

被引：1

作者：

Gao, Peng ^{[1
]}

Zhao, Liangyi ^{[2
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

MONATSHEFTE FUR MATHEMATIK | 2024年 / 203卷 / 01期

关键词：

Ratios conjecture; Mean values; Quadratic Hecke L-functions; ZETA-FUNCTIONS; SERIES; MOMENT;

D O I：

10.1007/s00605-023-01903-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke L-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of L-functions, obtaining an error term of size O(X1/2+epsilon).

引用

页码：63 / 90

页数：28

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