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K1 of products of Drinfeld modular curves and special values of L-functions

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 June 2010

Ramesh Sreekantan
Ramesh Sreekantan*
Affiliation:
Indian Statistical Institute, 8th Mile, Mysore Road, Jnana Bharathi, Bangalore 560 059, India (email: rameshsreekantan@gmail.com)
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Abstract

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Beilinson [Higher regulators and values of L-functions, Itogi Nauki i Tekhniki Seriya Sovremennye Problemy Matematiki Noveishie Dostizheniya (Current problems in mathematics), vol. 24 (Vserossiisky Institut Nauchnoi i Tekhnicheskoi Informatsii, Moscow, 1984), 181–238] obtained a formula relating the special value of the L-function of H2 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.

Keywords

Drinfeld modular curvesmotivic cohomologyspecial values of L-functions

MSC classification

Secondary: 11F52: Modular forms associated to Drinfel'd modules 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 886 - 918
Copyright
Copyright © Foundation Compositio Mathematica 2010

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