Conjectures for the integral moments and ratios of \(L\)-functions over function fields

DOI10.1016/j.jnt.2014.02.019zbMath1318.11083arXiv1407.3099OpenAlexW2090082281WikidataQ57937578 ScholiaQ57937578MaRDI QIDQ403285

Jonathan P. Keating, Julio C. Andrade

Publication date: 29 August 2014

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

Full work available at URL: https://arxiv.org/abs/1407.3099

zbMATH Keywords

function fields\(L\)-functionshyperelliptic curvesrandom matrix theorymoments of quadratic Dirichletratios of \(L\)-functions

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) Relations with random matrices (11M50)

Related Items (29)

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 ⋮ Average values of \(L\)-series for real characters in function fields ⋮ On the Northcott property of zeta functions over function fields ⋮ Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble ⋮ The Ratios Conjecture and upper bounds for negative moments of 𝐿-functions over function fields ⋮ A Refined Conjecture for the Variance of Gaussian Primes across Sectors ⋮ Conjectures for Moments Associated With Cubic Twists of Elliptic Curves ⋮ Moments of zeta functions associated to hyperelliptic curves over finite fields ⋮ Number fields and function fields: coalescences, contrasts and emerging applications ⋮ Secondary terms in the asymptotics of moments of \(L\)-functions ⋮ Rudnick and Soundararajan's theorem for function fields ⋮ Moments of traces of Frobenius of higher order Dirichlet $L$-functions over $\mathbb F_q[T$] ⋮ The size of wild Kloosterman sums in number fields and function fields ⋮ One-level density of zeros of Dirichlet \(L\)-functions over function fields ⋮ Moments of quadratic twists of elliptic curve \(L\)-functions over function fields ⋮ On the third moment of \(L(\frac{1}{2}, \chi_d)\). I: The rational function field case ⋮ Average values of \(L\)-functions in even characteristic ⋮ Correlation of shifted values of \(L\)-functions in the hyperelliptic ensemble ⋮ The integral moments and ratios of quadratic Dirichlet \(L\)-functions over monic irreducible polynomials in \(\mathbb{F}_q [T\)] ⋮ The integrated fourth moment of Dirichlet \(L\)-functions over rational function fields ⋮ The fourth moment of quadratic Dirichlet \(L\)-functions ⋮ A simple proof of the mean value of \(|K_2(\mathcal O)|\) in function fields ⋮ A note on the mean value of \(L(\frac{1}{2}, \chi)\) in the real hyperelliptic ensemble ⋮ A representation theory approach to integral moments of \(L\)-functions over function fields ⋮ Singularities and vanishing cycles in number theory over function fields ⋮ Polya-Vinogradov inequality for polynomial character sums over finite fields ⋮ The first moment of $L\bigl(\frac{1}{2},\chi\bigr)$ for real quadratic function fields ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields

Cites Work

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