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

Jeongho Park; Peter J. Cho

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

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arxiv 1802.01762 v2 pith:34TUEGRO submitted 2018-02-06 math.NT

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

Peter J. Cho , Jeongho Park This is my paper

classification math.NT

keywords densityone-levelconjecturecubicdirichletfamilyfunctionsratios

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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.

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

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