WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT -FUNCTIONS

Periods and Special Values of L-functions

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’...

Ratios of Periods for Tensor Product Motives

In this paper, we prove some period relations for the ratio of Deligne’s periods for certain tensor product motives. These period relations give a motivic interpretation for certain algebraicity results for ratios of successive critical values for Rankin–Selberg L-functions for GLn × GLn′ proved by Günter Harder and the second author.

Computing Special Values of Motivic L-Functions

We present an algorithm to compute values L(s) and derivatives L(s) of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Γ-factor is of the form A ∏d i=1 Γ( s+λj 2 ) with d arbitrary and complex λj , not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).

Values of L-Functions and Periods of Integrals

In this article, I present a conjecture (1.8, 2.8) relating the values of certain L-functions at certain integer points to the periods of integrals. The L-functions we consider here are those of motives a word to which we shall not attach a precise meaning. They include, notably, Artin L-functions, L-functions attached to algebraic Hecke characters (= Grossencharacter of type A0), and those att...

Multiple Zeta Values and Periods of Moduli