English

Low-lying zeros of cubic Dirichlet $L$-functions and the Ratios Conjecture

Number Theory 2019-01-23 v2

Abstract

We compute the one-level density for the family of cubic Dirichlet LL-functions when the support of the Fourier transform of a test function is in (1,1)(-1,1). We also establish the Ratios conjecture prediction for the one-level density for this family, and confirm that it agrees with the one-level density we obtain.

Keywords

Cite

@article{arxiv.1802.01762,
  title  = {Low-lying zeros of cubic Dirichlet $L$-functions and the Ratios Conjecture},
  author = {Peter J. Cho and Jeongho Park},
  journal= {arXiv preprint arXiv:1802.01762},
  year   = {2019}
}