Period Identities of CM Forms on Quaternion Algebras

automorphic forms;torus periods;theta lifts;Mathematics;Science;Mathematics

Chan, CharlotteSnowden, Andrew ;

University of Michigan

关键词: automorphic forms;    torus periods;    theta lifts;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/145838/charchan_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

A few decades ago, Waldspurger proved a groundbreaking identity between the central value of an L-function and the norm of a torus period. Combining this with the Jacquet--Langlands correspondence gives a relationship between the norm of torus periods arising from different quaternion algebras for automorphic forms attached to Hecke characters. In this setting, the torus and the quaternion algebras can be realized as dual reductive pairs that are compatible in a so-called seesaw. We exploit the theta correspondence to give a direct proof of the identity of the torus periods themselves.