English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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.

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in $$\mathbb {F}_{q}[T]$$