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^*

^*Corresponding author for this work

School of Mathematical Sciences

University of New South Wales

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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) .

Original language	English
Pages (from-to)	63-90
Number of pages	28
Journal	Monatshefte fur Mathematik
Volume	203
Issue number	1
DOIs	https://doi.org/10.1007/s00605-023-01903-5
State	Published - Jan 2024

Keywords

Mean values
Quadratic Hecke L-functions
Ratios conjecture

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10.1007/s00605-023-01903-5

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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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AU - Zhao, Liangyi

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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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EP - 90

JO - Monatshefte fur Mathematik

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IS - 1

ER -

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

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Keywords

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