Experimental Mathematics

The Quadratic Character Experiment

Jeffrey Stopple

Full-text: Open access

Abstract

A fast new algorithm is used compute the zeros of $10^6$ quadratic character $L$-functions for negative fundamental discriminants with absolute value $d>10^{12}$. 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.

Article information

Source
Experiment. Math., Volume 18, Issue 2 (2009), 193-200.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1259158429

Mathematical Reviews number (MathSciNet)
MR2549688

Zentralblatt MATH identifier
1226.11089

Subjects
Primary: 11Y16: Algorithms; complexity [See also 68Q25] 11Y35: Analytic computations

Keywords
Dirichlet $L$-functions low lying zeros

Citation

Stopple, Jeffrey. The Quadratic Character Experiment. Experiment. Math. 18 (2009), no. 2, 193--200. https://projecteuclid.org/euclid.em/1259158429


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