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FUNDAMENTAL CYCLE OF A PERIODIC BOX-BALL SYSTEM: A NUMBER THEORETICAL ASPECT

Published online by Cambridge University Press:  14 July 2005

TETSUJI TOKIHIRO  and
JUN MADA
TETSUJI TOKIHIRO
Affiliation:
Graduate school of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan
JUN MADA
Affiliation:
Graduate school of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan
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Abstract

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A number theoretical aspect of the fundamental cycle of a periodic box-ball system is investigated. Using the formulae for the fundamental cycle of a class of initial states, we point out that the asymptotic behaviour of the fundamental cycle is closely related to the celebrated Riemann hypothesis.

Keywords

37B15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue A , June 2005 , pp. 199 - 204
Copyright
2005 Glasgow Mathematical Journal Trust