The quadratic character experiment

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.

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

References in corpus (1)

• A Symplectic Test of the L-Functions Ratios Conjecture

Cited by in corpus (2)

• The effect of convolving families of L-functions on the underlying group symmetries
• An Orthogonal Test of the $L$-functions Ratios Conjecture, II