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

Let pi be an automorphic representation on GL(r, A_Q) for r=1, 2, or 3. Let dbe a fundamental discriminant and chi_d the corresponding quadratic Dirichletcharacter. We consider the question of the least d, relative to the data(level, weight or eigenvalue) of pi, such that the central value of the twistedL-series is nonzero, i.e. L(1/2, pi x chi_d) != 0. For example, let N be thelevel of pi. Using multiple Dirichlet series, we prove the nonvanishing of acentral twisted $L$-value with d << N^{1/2} for GL(1), d << N^1 for GL(2), andd << N^2 for GL(3), the last case assuming that a certain character isquadratic (see Theorem 1.13). We work over Q for simplicity but the methodgeneralizes to arbitrary number fields. We conjecture that in all cases thereshould be such a twist with d << N^epsilon. This would follow from aLindelof-type bound for a multiple Dirichlet series which does not have anEuler product, but is constructed from a Rankin-Selberg integral applied toautomorphic forms which are eigenfunctions of Hecke operators.

The first non-vanishing quadratic twist of an automorphic L-series