Vanishing of Dirichlet \(L\)-functions at the central point over function fields

DOI10.1216/rmj.2021.51.1615zbMath1496.11121arXiv2012.15319OpenAlexW3115452207MaRDI QIDQ2135971

Ravi Donepudi, Wanlin Li

Publication date: 10 May 2022

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.15319

zbMATH Keywords

\(L\)-functionscyclotomic function fieldsChowla's conjectureabelian varieties over finite fieldszeta functions of curvesCarlitz extensions

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta functions and (L)-functions (11S40) Cyclotomy (11T22) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (1)

On the vanishing of twisted \(L\)-functions of elliptic curves over rational function fields

Cites Work

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• Squarefree values of multivariable polynomials
• Vanishing of hyperelliptic \(L\)-functions at the central point
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Dirichlet \(L\)-functions of quadratic characters of prime conductor at the central point
• Nonvanishing of hyperelliptic zeta functions over finite fields
• Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points
• Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble
• Nonvanishing for cubic L-functions
• Numbers of solutions of equations in finite fields

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