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

Peng Gao; Liangyi Zhao

doi:10.1016/j.indag.2025.07.001

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

Number Theory 2025-07-15 v3

Authors: Peng Gao , Liangyi Zhao

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Abstract

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.

Keywords

l-functions ratios conjecture cubic hecke l-functions prime moduli multiple dirichlet series generalized riemann hypothesis first moment one-level density

Cite

@article{arxiv.2311.08626,
  title  = {Ratios conjecture of cubic $L$-functions of prime moduli},
  author = {Peng Gao and Liangyi Zhao},
  journal= {arXiv preprint arXiv:2311.08626},
  year   = {2025}
}

Comments

14 pages, revised with accordance to the referee's comments and suggestions

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

Abstract

Keywords

Cite

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