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2009 The Quadratic Character Experiment
Jeffrey Stopple
Experiment. Math. 18(2): 193-200 (2009).

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.

Citation

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Jeffrey Stopple. "The Quadratic Character Experiment." Experiment. Math. 18 (2) 193 - 200, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1226.11089
MathSciNet: MR2549688

Subjects:
Primary: 11Y16, 11Y35

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 2 • 2009
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