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arXiv · 1802.01762

Low-lying zeros of cubic Dirichlet $L$-functions and the Ratios Conjecture

Peter J. Cho·Jeongho Park
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Abstract

We compute the one-level density for the family of cubic Dirichlet $L$-functions when the support of the Fourier transform of a test function is in $(-1,1)$. We also establish the Ratios conjecture prediction for the one-level density for this family, and confirm that it agrees with the one-level density we obtain.

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Peter J. Cho, Jeongho Park. 2018-02-06. Low-lying zeros of cubic Dirichlet $L$-functions and the Ratios Conjecture. https://arxiv.org/abs/1802.01762

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