Ratios conjecture for quadratic Hecke L-functions in the Gaussian field-Reference-Cited by-同舟云学术

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

Published:2023-09-27 Issue:1 Volume:203 Page:63-90
ISSN:0026-9255
Container-title:Monatshefte für Mathematik
language:en
Short-container-title:Monatsh Math

Author:

Gao Peng,Zhao Liangyi^ORCID

Abstract

AbstractWe 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

$$O(X^{1/2+\varepsilon })$$

O ( X 1 / 2 + ε ) .

Funder

University of New South Wales

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00605-023-01903-5.pdf

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