Period Relations for Standard $L$-functions of Symplectic Type

Abstract

This article is to understand the critical values of $L$-functions $L(s,\Pi \otimes \chi )$ and to establish the relation of the relevant global periods at the critical places. Here $\Pi$ is an irreducible regular algebraic cuspidal automorphic representation of ${\mathrm{GL}}_{2n}(\mathbb{A})$ of symplectic type and $\chi$ is a finite order automorphic character of ${\mathrm{GL}}_1(\mathbb{A})$, with $\mathbb{A}$ is the ring of adeles of a number field $\mathrm{k}$.

References in corpus (1)

• Cohomologically induced distinguished representations and cohomological test vectors

Cited by in corpus (1)

• Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$