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

TL;DR

This paper proves a formula relating special L-values to motivic cohomology regulators for products of Drinfeld modular curves, extending Beilinson's results from classical modular curves to the function field setting.

Contribution

It establishes a new formula connecting L-values and motivic cohomology for Drinfeld modular curves, supporting analogous conjectures in the function field context.

Findings

Proves a Beilinson-type formula for Drinfeld modular curves.

Provides evidence for conjectures on special L-values in function fields.

Extends classical results to the setting of Drinfeld modules.

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.