Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field
Number Theory
2024-01-17 v2
Abstract
We develope the -functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke -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 -functions, obtaining an error term of size .
Keywords
Cite
@article{arxiv.2210.08840,
title = {Ratios conjecture for quadratic Hecke $L$-functions in the Gaussian field},
author = {Peng Gao and Liangyi Zhao},
journal= {arXiv preprint arXiv:2210.08840},
year = {2024}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:2207.03746