Elliptic Functions according to Eisenstein and Kronecker / Edition 1by Andre Weil
Pub. Date: 12/17/1998
Publisher: Springer Berlin Heidelberg
Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).
- Springer Berlin Heidelberg
- Publication date:
- Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, #88
- Edition description:
- Reprint of the 1st ed. Heidelberg Berlin 1976.
- Product dimensions:
- 6.26(w) x 9.22(h) x 0.29(d)
Table of ContentsI 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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