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Theory of The Generalized Bernoulli-Hurwitz Numbers for The Algebraic Functions of Cyclotomic Type and The Universal Bernoulli Numbers

Yoshihiro Ônishi
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Abstract

Hurwitz numbers are the Laurent coefficients of an elliptic function $\wp(u)$ of cyclotomic type, and they are natural generalization of the Bernoulli numbers. This paper gives new generalization of Bernoulli and Hurwitz numbers for higher genus cases. They satisfy completely von Staudt-Clausen type theorem, an extension of von Staudt second theorem, and Kummer type congruence relation. The present paper is revised and combined version of math.NT/0304377 and math.NT/0312178 containing many numerical examples.

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Yoshihiro Ônishi. 2004-06-15. Theory of The Generalized Bernoulli-Hurwitz Numbers for The Algebraic Functions of Cyclotomic Type and The Universal Bernoulli Numbers. https://arxiv.org/abs/math/0406096

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