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• W2883119704 abstract "In this paper we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of $L$-functions. We also adapt to the function setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of $L$-functions. Specifically, the focus of this paper is on the family of quadratic Dirichlet $L$-functions $L(s,chi_{P})$ where the character $chi$ is defined by the Legendre symbol for polynomials in $mathbb{F}_{q}[T]$ with $mathbb{F}_{q}$ a finite field of odd cardinality and the averages are taken over all monic and irreducible polynomials $P$ of a given odd degree. As an application we also compute the formula for the one-level density for the zeros of these $L$-functions." @default.
• W2883119704 created "2018-08-03" @default.
• W2883119704 creator A5022272914 @default.
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• W2883119704 creator A5053091859 @default.
• W2883119704 date "2018-07-17" @default.
• W2883119704 modified "2023-10-13" @default.
• W2883119704 title "The Integral Moments and Ratios of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $mathbb{F}_{q}[T]$" @default.
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• W2883119704 hasPublicationYear "2018" @default.
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