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AuthorWeil, Andrรฉ. author
TitleElliptic Functions according to Eisenstein and Kronecker [electronic resource] / by Andrรฉ Weil
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1976
Connect tohttp://dx.doi.org/10.1007/978-3-642-66209-6
Descript IX, 94 p. online resource

SUMMARY

"As a contribution to the history of mathematics, this is a model of its kind. While adhering to the basic outlook of Eisenstein and Kronecker, it provides new insight into their work in the light of subsequent developments, right up to the present day. As one would expect from this author, it also contains some pertinent comments looking into the future. It is not however just a chapter in the history of our subject, but a wide-ranging survey of one of the most active branches of mathematics at the present time. The book has its own very individual flavour, reflecting a sort of combined Eisenstein-Kronecker-Weil personality. Based essentially on Eisenstein's approach to elliptic functions via infinite series over lattices in the complex plane, it stretches back to the very beginnings on the one hand and reaches forward to some of the most recent research work on the other. (...) The persistent reader will be richly rewarded." A. Frรถhlich, Bulletin of the London Mathematical Society, 1978


CONTENT

I EISENSTEIN -- I Introduction -- II Trigonometric functions -- III The basic elliptic functions -- IV Basic relations and infinite products -- V Variation I -- VI Variation II -- II KRONECKER -- VII Prelude to Kronecker -- VIII Kroneckerโ{128}{153}s double series -- IX Finale: Allegro con brio (Pellโ{128}{153}s equation and the Chowla-Selberg formula) -- Index of Notations


Mathematics Number theory Mathematics Number Theory



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