K1 of products of Drinfeld Modular Curves and Special Values of L-functions

Abstract

Let $X_0(I)$ be the Drinfeld's modular curve with level $I$ structure, where $I$ is a monic square-free ideal in $\F_{q}[T]$. In this paper we show the existence of an element in the motivic cohomology group $H^3_{\M}(X_0(I) \times X_0(I),\Q(2))$ whose regulator is related to a special value of a Ranking-Selberg convolution $L$-function. This result is the function field analogue of a theorem of Beilinson for the self product of a modular curve.