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Division polynomials and multiplication formulae of Jacobian varieties of dimension 2

Published online by Cambridge University Press:  21 October 2005

NAOKI KANAYAMA
NAOKI KANAYAMA
Affiliation:
Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan. e-mail: [email protected]
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Abstract

D. Grant gave a set of defining equations and the addition formulae on the Jacobian varieties of hyperelliptic curves of the form $y^2=x^{5}+\cdots$, using the $\sigma$-function and hyperelliptic functions. In this paper, using these functions, we give the n-multiplication formulae on the Jacobian varieties of hyperelliptic curves of the form $y^2=x^{5}+\cdots$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 3 , November 2005 , pp. 399 - 409
Copyright
2005 Cambridge Philosophical Society

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