Elliptic functions according to Eisenstein and Kronecker
Author(s)
Bibliographic Information
Elliptic functions according to Eisenstein and Kronecker
（Classics in mathematics）
Springer-Verlag, c1999
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Note
Reprint of the 1976 edition
Originally published as Vol.88 of the Ergebnisse der Mathematik und ihrer Grenzgebiete -- t.p. verso
Description and Table of Contents
Description
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.
Table of Contents
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 Kronecker's double series.- IX Finale: Allegro con brio (Pell's equation and the Chowla-Selberg formula).- Index of Notations.
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