论文信息 - The Quadratic Character Experiment

The Quadratic Character Experiment

A fast new algorithm is used compute the zeros of 106 quadratic character L-functions for negative fundamental discriminants with absolute value d > 1012. 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.

Jeffrey Stopple | J. Stopple

[1] D. Farmer,et al. Autocorrelation of ratios of L-functions , 2007, 0711.0718.

[2] On small zeros of Dirichlet $L$-functions , 1975 .

[3] P. Sarnak,et al. Zeroes of zeta functions and symmetry , 1999 .

[4] N. Snaith,et al. Applications of the L‐functions ratios conjectures , 2005, math/0509480.

[5] Åke Björck,et al. Numerical Methods , 2020, Markov Renewal and Piecewise Deterministic Processes.

[6] Steven J. Miller,et al. A Symplectic Test of the L-Functions Ratios Conjecture , 2007, 0704.0927.

[7] Jeffrey Stopple. Computing L-functions with large conductor , 2007, Math. Comput..

[8] F. A. Seiler,et al. Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[9] M. Jutila. On character sums and class numbers , 1973 .

[10] D. R. Heath-Brown,et al. The Theory of the Riemann Zeta-Function , 1987 .

[11] Michael O. Rubinstein,et al. Evidence for a Spectral Interpretation of the Zeros of , 1998 .

[12] C. Snyder,et al. Small zeros of quadratic L-functions , 1993, Bulletin of the Australian Mathematical Society.

[13] A. Booth. Numerical Methods , 1957, Nature.

[14] Mark Watkins,et al. Class numbers of imaginary quadratic fields , 2003, Math. Comput..