Journal of the Ramanujan Mathematical Society

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Kronecker’s Jugendtraum and Ring Sine Functions


Affiliations
1 Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo-152-8551, Japan
2 Graduate School of Mathematics, Kyushu University, Fukuoka-812-8581, Japan
     

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We present the notion of the sine function of a ring, and we calculate some examples. This contains the case of the rational integer ring and the case of the imaginary quadratic integer rings. These results indicate such a sine function of a ring would be a good candidate to the aforementioned special function for the Kronecker’s Jugendtraum.
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  • Kronecker’s Jugendtraum and Ring Sine Functions

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Authors

Nobushige Kurokawa
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo-152-8551, Japan
Eva-Marie Muller-Stuler
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo-152-8551, Japan
Hiroyuki Ochiai
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo-152-8551, Japan
Masato Wakayama
Graduate School of Mathematics, Kyushu University, Fukuoka-812-8581, Japan

Abstract


We present the notion of the sine function of a ring, and we calculate some examples. This contains the case of the rational integer ring and the case of the imaginary quadratic integer rings. These results indicate such a sine function of a ring would be a good candidate to the aforementioned special function for the Kronecker’s Jugendtraum.