K_1 of products of Drinfeld modular curves and special values of L-functions

Abstract

Beilinson obtained a formula relating the special value of the L-function of H^2 of a product of modular curves to the regulator of an element of a motivic cohomology group - thus providing evidence for his general conjectures on special values of L-functions. In this paper we prove a similar formula for the L-function of the product of two Drinfeld modular curves providing evidence for an analogous conjecture in the case of function fields.

34 pages, 2 figures. To appear in Compositio Mathematica. This is a completely revised and improved version of a earlier preprint with C.Consani (arXiv:math/0303130)