The Quadratic Character Experiment
Stopple, Jeffrey
Experiment. Math., Tome 18 (2009) no. 1, p. 193-200 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Dirichlet $L$-functions,  low lying zeros,  11Y16,  11Y35 
@article{1259158429,
     author = {Stopple, Jeffrey},
     title = {The Quadratic Character Experiment},
     journal = {Experiment. Math.},
     volume = {18},
     number = {1},
     year = {2009},
     pages = { 193-200},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1259158429}
}

Stopple, Jeffrey. The Quadratic Character Experiment. Experiment. Math., Tome 18 (2009) no. 1, pp.  193-200. http://gdmltest.u-ga.fr/item/1259158429/