n-level density of the low-lying zeros of primitive Dirichlet L-functions

Chandee, Vorrapan; Lee, Yoonbok

doi:10.1016/j.aim.2020.107185

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2022

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“…For various families, the conjecture has been tested and all the results have supported it. Since it is impossible to give a complete list, we name just a few of them [1,2,4,16,25,29,30].…”

Section: Introductionmentioning

confidence: 99%

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

Cho

Park

2019

Journal of Mathematical Analysis and Applications

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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 the associated 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.In this work, we study the low-lying zeros of cubic Dirichlet L-functions. Let φ be an even Schwartz function whose Fourier transform is compactly supported. For a cubic Dirichlet character χ, let ρ denote the nontrivial zeros of L(χ, s) in the critical strip. Define

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“…For various families, the conjecture has been tested and all the results have supported it. Since it is impossible to give a complete list, we name just a few of them [1,2,4,16,25,29,30].…”

Section: Introductionmentioning

confidence: 99%