Premium
On central critical values of Rankin‐type L ‐functions over global function fields
Author(s) -
Chuang ChihYun,
Wei FuTsun,
Yu Jing
Publication year - 2017
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12009
Subject(s) - mathematics , type (biology) , function (biology) , pure mathematics , geology , biology , evolutionary biology , paleontology
Abstract The aim of this paper is to study the central critical value of Rankin‐type L ‐functions coming from ‘Drinfeld‐type’ automorphic cusp forms convolved with ‘imaginary’ quadratic characters. Rankin–Selberg method provides us with a very explicit functional equation for these Rankin‐type L ‐functions. When the ‘root number’ in question is positive, we derive a Gross‐type formula over arbitrary global function field. Via the theta series constructed from definite pure quaternions, we then establish a Shimura correspondence between Drinfeld‐type forms and metaplectic forms onSL ∼ 2 . Having this correspondence at hand leads us to an explicit Waldspurger‐type formula in this setting.