Period Relations for Standard L-functions of Symplectic Type

2019/09/08 by Jiang, Dihua, Sun, Binyong, Tian, Fangyang · 1 citation
#11F67 #22E45 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1909.03476

Abstract

This article is to understand the critical values of L-functions L(s,Π⊗ χ) and to establish the relation of the relevant global periods at the critical places. Here Π is an irreducible regular algebraic cuspidal automorphic representation of GL_2n(\mathbb A) of symplectic type and χ is a finite order automorphic character of GL₁(\mathbb A), with \mathbb A is the ring of adeles of a number field \mathrm k.

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• Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh

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