PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS

Waldspurger’s formula gives an identity between the norm of a torus period and an $L$ -function of the twist of an automorphic representation on GL(2). For any two Hecke characters of a fixed quadratic extension, one can consider the two torus periods coming from integrating one character against the automorphic induction of the other. Because the corresponding $L$ -functions agree, (the norms of) these periods—which occur on different quaternion algebras—are closely related. In this paper, we give a direct proof of an explicit identity between the torus periods themselves.

Models of Representations and Langlands Functoriality

In this article we explore the interplay between two generalizations of the Whittaker model, namely the Klyachko models and the degenerate Whittaker models, and two functorial constructions, namely base change and automorphic induction, for the class of unitarizable and ladder representations of the general linear groups.

On the Kottwitz-Shelstad normalization of transfer factors for automorphic induction for GLn

Automorphic induction for GLn is a case of endoscopic transfer, and its character identity was established by Henniart and Herb, up to a constant of proportionality. We determine this constant in terms of the Kottwitz-Shelstad normalization of transfer factors, which involves certain ε-factors.