Ratios conjecture of cubic $L$-functions of prime moduli

Fuente: arXiv
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Auteurs principaux: Gao, Peng, Zhao, Liangyi
Format: Preprint
Publié: 2023
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author Gao, Peng
Zhao, Liangyi
author_facet Gao, Peng
Zhao, Liangyi
contents We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions.
format Preprint
id arxiv_https___arxiv_org_abs_2311_08626
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Ratios conjecture of cubic $L$-functions of prime moduli
Gao, Peng
Zhao, Liangyi
Number Theory
11M06, 11M41
We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of $L$-functions.
title Ratios conjecture of cubic $L$-functions of prime moduli
topic Number Theory
11M06, 11M41
url https://arxiv.org/abs/2311.08626