Periods and Special Values of L-functions
نویسنده
چکیده
Introduction 1 1. Modular forms, congruences and the adjoint L-function 2 2. Quaternion algebras and the Jacquet-Langlands correspondence 6 3. Integral period relations for quaternion algebras over Q 8 4. The theta correspondence 12 5. Arithmetic of the Shimizu lift and Waldspurger’s formula 16 6. Hilbert modular forms, Shimura’s conjecture and a refined version 19 7. Unitary groups and Harris’ proof of algebraicity 21 8. Quaternionic unitary groups 21 Appendices 27 A. Outline of student projects 27 B. Computing on Shimura Curves I: Expansions at CM points 32 C. Computing on Shimura curves II: Implementing the Shimizu lifting (by PAUL NELSON) 44 D. Norms of definite quaternionic modular forms in Magma: A primer (by JOHN VOIGHT) 57 References 68
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