THE FOURTH MOMENT OF DIRICHLET L-FUNCTIONS FOR THE RATIONAL FUNCTION FIELD

Nattalie Tamam

Type: Article

Publication Date: 2013-08-06

Citations: 15

DOI: https://doi.org/10.1142/s1793042113500899

Abstract

We study the moments of the Dirichlet L-function when defined over the polynomial ring over finite fields. We obtain an asymptotic formula of the fourth moment for the central value of these Dirichlet L-functions. In addition, we find a lower bound for the 2k th moment of these L-functions. These results agree up to constants with the polynomial ring analog of the Keating and Snaith Conjecture for the asymptotic of leading terms.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (16)

Action	Title	Year	Authors
+	A Brun-Titschmarsh theorem for multiplicative functions.	1980	Peter Shiu
+ PDF Chat	Zeros of Dirichlet $L$-functions	1992	R. Balasubramanian V. Kumar Murty
+	Statistical Theory of the Energy Levels of Complex Systems. I	1962	Freeman J. Dyson
+ PDF Chat	Lower bounds for moments of <i>L</i> -functions	2005	Zeév Rudnick K. Soundararajan
+ PDF Chat	Zeroes of zeta functions and symmetry	1999	Nicholas Katz Peter Sarnak
+	Sieve methods for polynomial rings over finite fields	1983	William A. Webb
+ PDF Chat	Random Matrix Theory and ζ(1/2+ it)	2000	Jonathan P. Keating N. C. Snaith
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+	The Fourth Power Mean of Dirichlet's L-Functions	1981	D. R. Heath‐Brown
+ PDF Chat	On a Question of Keating and Rudnick about Primitive Dirichlet Characters with Squarefree Conductor	2012	Nicholas M. Katz