On algebraicity of special values of $L$-functions for $mathrm{SO}(mathbf{V})timesmathrm{GL}_{2}$ (Algebraic Number Theory and Related Topics 2013)

Abstract

In this paper, we announce the result of the joint work [8] with Masaaki Furusawa, in which we state a conjecture (see Conjecture 2) on the algebraicity of special values of tensor product L-functions for automorphic representations of SO(V) and mathrm{G}mathrm{L}_{2} explicating Deligne periods and we show this conjecture at various critical points under certain assumption on the weight (see Theorem 3.1. This algebraicity result is a generalization of our previous result [7, Theorem 1] with respect to critical points and infinity types of automorphic representations of SO(V).