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

Peng Gao; Liangyi Zhao

doi:10.1007/s00605-023-01903-5

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

Peng Gao
, Liangyi Zhao^*

^*此作品的通讯作者

数学科学学院

School of Mathematics and Statistics
University of New South Wales

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

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⁺^ε) .

源语言	英语
页（从-至）	63-90
页数	28
期刊	Monatshefte fur Mathematik
卷	203
期	1
DOI	https://doi.org/10.1007/s00605-023-01903-5
出版状态	已出版 - 1月 2024

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abstract = "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+ε) .",

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N2 - 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+ε) .

AB - 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+ε) .

KW - Mean values

KW - Quadratic Hecke L-functions

KW - Ratios conjecture

UR - https://www.scopus.com/pages/publications/85173048445

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DO - 10.1007/s00605-023-01903-5

M3 - 文章

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JO - Monatshefte fur Mathematik

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

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