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Automorphic functions for a Kleinian group

Masaaki Yoshida

Geometry & Topology Monographs 13 (2008) 483–497

DOI: 10.2140/gtm.2008.13.483

arXiv: 0904.1022

Abstract

In the paper ‘Automorphic functions for a Whitehead-complement group’, [Osaka J Math 43 (2006) 63–77] Matsumoto, Nishi and Yoshida constructed automorphic functions on real 3–dimensional hyperbolic space for a Kleinian group called the Whitehead-link-complement group. For a Kleinian group (of the first kind), no automorphic function/form has been studied before. In this note, their motivation is presented with a historical background.

Dedicated to Professor Fred Cohen on his sixtieth birthday

Keywords

Whitehead link, hyperbolic structure, automorphic forms, theta functions, hypergeometric differential equation

Mathematical Subject Classification

Primary: 11F55, 14P05

Secondary: 57M25

References
Publication

Received: 24 November 2005
Revised: 12 December 2006
Accepted: 19 January 2007
Published: 19 March 2008

Authors
Masaaki Yoshida
Department of Mathematics
Kyushu University
Fukuoka 810-8560
Japan