This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.

About the Author
Atsushi Ichino, Kyoto University, Japan, and Kartik Prasanna, University of Michigan, Ann Arbor, MI.


Book Information
ISBN 9781470448943
Author Atsushi Ichino
Format Paperback
Page Count 220
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 395g