Lower bounds for moments of L-functions.

Some Lower Bounds for Estrada Index

Lower Bounds for Moments of L-functions: Symplectic and Orthogonal Examples

An important problem in number theory asks for asmptotic formulas for the moments of central values of L-functions varying in a family. This problem has been intensively studied in recent years, and thanks to the pioneering work of Keating and Snaith [7], and the subsequent contributions of Conrey, Farmer, Keating, Rubinstein and Snaith [1], and Diaconu, Goldfeld and Hoffstein [3] there are now...

Bounds for CDFs of Order Statistics Arising from INID Random Variables

In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a main concern for researchers. A cumulative distribution function (CDF) of these random variables (Fi:n) is a complex manipulating, long time consuming and a software-intensive tool that takes more and more times. Therefore, obtaining approximations a...

Rudnick and Soundararajan's theorem for function fields

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet L–functions. We establish lower bounds for the moments of quadratic Dirichlet L–functions associated to hyperelliptic curves of genus g over a fixed finite field Fq in the large genus g limit.

Lower Bounds for Moments of Automorphic L-functions over Short Intervals

Let L(s, π) be the principal L-function attached to an irreducible unitary cuspidal automorphic representation π of GLm(AQ). The aim of the paper is to give a simple method to show the lower bounds of mean value for automorphic L-functions over short intervals.