Mean value theorems for L-functions over prime polynomials for the rational function field

DOI10.4064/aa161-4-4zbMath1286.11097arXiv1401.0418OpenAlexW2964104844MaRDI QIDQ2867692

Jonathan P. Keating, Julio C. Andrade

Publication date: 20 December 2013

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0418

zbMATH Keywords

hyperelliptic curvefunction fieldfinite fieldsmoments of quadratic Dirichlet L-functionprime polynomial

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta and (L)-functions in characteristic (p) (11M38) Relations with random matrices (11M50)

Related Items (16)

Dirichlet \(L\)-functions of quadratic characters of prime conductor at the central point ⋮ The second and third moment of \(L(1/2,\chi)\) in the hyperelliptic ensemble ⋮ The fourth moment of quadratic Dirichlet \(L\)-functions over function fields ⋮ The mixed second moment of quadratic Dirichlet \(L\)-functions over function fields ⋮ Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli ⋮ Average values of \(L\)-series for real characters in function fields ⋮ Small zeros of Dirichlet \(L\)-functions of quadratic characters of prime modulus ⋮ Conjectures for the integral moments and ratios of \(L\)-functions over function fields ⋮ Mean values of derivatives of L-functions in function fields: III ⋮ Nonvanishing of hyperelliptic zeta functions over finite fields ⋮ Average values of \(L\)-functions in even characteristic ⋮ Type-I contributions to the one and two level densities of quadratic Dirichlet \(L\)-functions over function fields ⋮ The fourth moment of derivatives of Dirichlet \(L\)-functions in function fields ⋮ The integral moments and ratios of quadratic Dirichlet \(L\)-functions over monic irreducible polynomials in \(\mathbb{F}_q [T\)] ⋮ Moments of Dirichlet \(L\)-functions with prime conductors over function fields ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields

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