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Addition theorem of Abel type for hyper-logarithms

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Aomoto
Kazuhiko Aomoto*
Affiliation:
Department of Mathematics, Faculty of Science, Nogoya University, Chikusa-ku, Nagoya 464, Japan
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Several kinds of generalizations of classical Abel Theorem in algebraic curves are known, for example see [12] and [13]. It seems to the author these are all regarded as local relations among rational differential forms. In this article we shall try to generalize Abel Theorem for integrals of rational forms in some specific cases where these can be described in terms of hyper-logarithms (for the definition see [3] and [4], Theorem 2). Trigonometric functions have been generalized to higher dimensional cases by L. Schläfli who has obtained a very important variational formula related to the volume of a spherical simplex [16].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 55 - 71
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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