One-level density of zeros of Dirichlet \(L\)-functions over function fields

DOI10.1016/j.jnt.2023.11.015arXiv2211.00076OpenAlexW4390674921MaRDI QIDQ6190999

Hua Lin

Publication date: 8 February 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.00076

zbMATH Keywords

function fieldsDirichlet \(L\)-functionsone-level densityKatz and Sarnak's philosophy

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Zeta and (L)-functions in characteristic (p) (11M38) Zeta functions and (L)-functions of function fields (11R59)

Cites Work

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• Conjectures for the integral moments and ratios of \(L\)-functions over function fields
• Mean values with cubic characters
• Autocorrelation of ratios of \(L\)-functions
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Moments of central values of quartic Dirichlet \(L\)-functions
• Hilbert spaces and low-lying zeros of \(L\)-functions
• Low-lying zeros of cubic Dirichlet \(L\)-functions and the ratios conjecture
• Traces of high powers of the Frobenius class in the hyperelliptic ensemble
• Zeroes of zeta functions and symmetry
• Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble
• Nonvanishing for cubic L-functions
• One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke -functions
• Small zeros of quadratic L-functions
• ON THE DISTRIBUTION OF THE RATIONAL POINTS ON CYCLIC COVERS IN THE ABSENCE OF ROOTS OF UNITY
• THE FOURTH MOMENT OF DIRICHLET L-FUNCTIONS FOR THE RATIONAL FUNCTION FIELD

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