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

We study the family of Dirichlet $L$-functions of all even primitivecharacters of conductor at most $Q$, where $Q$ is a parameter tending to$\infty$. For an arbitrary positive integer $k$, we approximate the twisted$2k$th moment of this family by using Dirichlet polynomial approximations of$L^k(s,\chi)$ of length $X$, with $Q<X<Q^2$. Assuming the GeneralizedLindel\"{o}f Hypothesis, we prove an asymptotic formula for theseapproximations of the twisted moments. Our result agrees with the prediction ofConrey, Farmer, Keating, Rubinstein, and Snaith for this family of$L$-functions, and provides the first rigorous evidence beyond the diagonalterms for their conjectured asymptotic formula for the general $2k$th moment ofthis family.

Twisted $2k$th moments of primitive Dirichlet $L$-functions: beyond the diagonal