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

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

2004-06-06

arxiv.org/abs/math/0406096v5

Mathematics

Number Theory

AMS-TeX, 91 pages. Cleaned up several typos in old versions

Scientific paper

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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