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On Schottky groups arising from the hypergeometric equation with imaginary exponents |
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| Authors: | Takashi Ichikawa Masaaki Yoshida |
| Institution: | Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502 Japan ; Department of Mathematics, Kyushu University, Fukuoka 810-8560 Japan |
| Abstract: | In an article by Sasaki and Yoshida (2000), we encountered Schottky groups of genus 2 as monodromy groups of the hypergeometric equation with purely imaginary exponents. In this paper we study automorphic functions for these Schottky groups, and give a conjectural infinite product formula for the elliptic modular function  . |
| Keywords: | Hypergeometric equation monodromy group Schwarzian derivative reflection principle Schottky group automorphic functions infinite product $\lambda$ function |
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