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

• Autorzy: Julio C. Andrade , Jonathan P. Keating
• Języki publikacji: EN

Abstrakty

EN

The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these L-functions.

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 11M50: Relations with random matrices
• 11M38: Zeta and L -functions in characteristic p
• 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 4
• Strony: 371-385

Daty

wydano

2013

Twórcy

autor

Julio C. Andrade

• Institute for Computational and Experimental, Research in Mathematics (ICERM), Brown University, 121 South Main Street, Providence, RI 02903, U.S.A.

autor

Jonathan P. Keating

• School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

Identyfikatory

DOI

10.4064/aa161-4-4