Ratios conjecture for quadratic twists of modular L-functions

Peng Gao; Liangyi Zhao

doi:10.1007/s40993-024-00544-3

Ratios conjecture for quadratic twists of modular L-functions

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

1 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 twist of modular L-functions using multiple Dirichlet series under the generalized Riemann hypothesis.

Original language	English
Article number	54
Journal	Research in Number Theory
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/s40993-024-00544-3
State	Published - Sep 2024

Keywords

11M06
11M41
Modular L-functions
Quadratic twist
Ratios conjecture

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10.1007/s40993-024-00544-3

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title = "Ratios conjecture for quadratic twists of modular L-functions",

abstract = "We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular L-functions using multiple Dirichlet series under the generalized Riemann hypothesis.",

keywords = "11M06, 11M41, Modular L-functions, Quadratic twist, Ratios conjecture",

author = "Peng Gao and Liangyi Zhao",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",

year = "2024",

month = sep,

doi = "10.1007/s40993-024-00544-3",

language = "英语",

volume = "10",

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AU - Gao, Peng

AU - Zhao, Liangyi

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/9

Y1 - 2024/9

N2 - We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular L-functions using multiple Dirichlet series under the generalized Riemann hypothesis.

AB - We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular L-functions using multiple Dirichlet series under the generalized Riemann hypothesis.

KW - 11M06

KW - 11M41

KW - Modular L-functions

KW - Quadratic twist

KW - Ratios conjecture

UR - https://www.scopus.com/pages/publications/85195445898

U2 - 10.1007/s40993-024-00544-3

DO - 10.1007/s40993-024-00544-3

M3 - 文章

AN - SCOPUS:85195445898

SN - 2363-9555

VL - 10

JO - Research in Number Theory

JF - Research in Number Theory

IS - 3

M1 - 54

ER -

Ratios conjecture for quadratic twists of modular L-functions

Abstract

Keywords

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