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!ALGEBRAICITY AND TRANSCENDENCY OF BASIC SPECIAL VALUES OF SHINTANI’S DOUBLE SINE FUNCTIONS

Published online by Cambridge University Press:  30 May 2006

Nobushige Kurokawa  and
Masato Wakayama
Nobushige Kurokawa
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama Meguro, Tokyo, 152-0033, Japan (kurokawa@math.titech.ac.jp)
Masato Wakayama
Affiliation:
Faculty of Mathematics, Kyushu University, Hakozaki Fukuoka 812-8581, Japan (wakayama@math.kyushu-u.ac.jp)
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Abstract

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We study algebraicity and transcendency of certain basic special values of the double sine functions due to Hölder and Shintani by employing the zeta regularized product expressions.

Keywords

Primary 11M36algebraicitytranscendencydouble sine function
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 361 - 366
Copyright
Copyright © Edinburgh Mathematical Society 2006