English

The quadratic character experiment

Number Theory 2010-06-30 v3

Abstract

A fast new algorithm is used compute the zeros of the quadratic character L-functions for all negative fundamental discriminants with absolute value 10^12<d<10^12+10^7. These are compared to the 1-level density, including various lower order terms. These terms come from, on the one hand the Explicit Formula, and on the other the L-functions Ratios Conjecture. The latter give a much better fit to the data, providing numerical evidence for the conjecture.

Keywords

Cite

@article{arxiv.0802.4255,
  title  = {The quadratic character experiment},
  author = {Jeffrey Stopple},
  journal= {arXiv preprint arXiv:0802.4255},
  year   = {2010}
}

Comments

This postscript to the published version is based on the additional data generated during the process of refereeing, revision and publication - about three times as much as in the published version

R2 v1 2026-06-21T10:16:54.220Z