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math.NT2023

A Note on Twisted Moments of Dirichlet -functions

J. C. Andrade, J. MacMillan

In this paper, we establish an asymptotic formula for the twisted second moments of Dirichlet -functions with one and two twists when averaged over all primitive Dirichlet chara…

math.NT2021

Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

J. MacMillan

In this paper, we extend to the function field setting the heuristics developed by Conrey, Farmer, Keating, Rubinstein and Snaith for the integral moments of L-functions. Also, we…

math.NT2020

Rudnick and Soundarajan's Theorem over Prime Polynomials for the Rational Function Field

J. MacMillan

In this paper, we use the methods of Andrade, Rudnick and Soundarajan to prove a Theorem about Lower bounds of moments of quadratic Dirichlet L-functions associated to monic irredu…

math.NT2019

Remark on a Simple Proof of the Mean Value of in Function Fields

J. MacMillan

Let denote a finite field of odd cardinality , the polynomial ring over and the rational function…

math.NT2019

The First Moment of for Real Quadratic Function Fields

J. C. Andrade, J. MacMillan

In this paper we use techniques first introduced by Florea to improve the asymptotic formula for the first moment of the quadratic Dirichlet L-functions over the rational function…