Elliptic Functions according to Eisenstein and Kronecker

Andre Weil (Autor)

Buch | Softcover

IX, 94 Seiten

1998 | Reprint of the 1st ed. Heidelberg Berlin 1976.
Springer Berlin (Verlag)
978-3-540-65036-2 (ISBN)

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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 (...).

Biography of André Weil André Weil was born on May 6, 1906 in Paris. After studying mathematics at the École Normale Supérieure and receiving a doctoral degree from the University of Paris in 1928, he held professorial positions in India, France, the United States and Brazil before being appointed to the Institute for Advanced Study, Princeton in 1958, where he remained until he died on August 6, 1998. André Weil's work laid the foundation for abstract algebraic geometry and the modern theory of abelian varieties. A great deal of his work was directed towards establishing the links between number theory and algebraic geometry and devising modern methods in analytic number theory. Weil was one of the founders, around 1934, of the group that published, under the collective name of N. Bourbaki, the highly influential multi-volume treatise Eléments de mathématique.

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.

Erscheint lt. Verlag	3.12.1998
Reihe/Serie	Classics in Mathematics
Zusatzinfo	IX, 94 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	186 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	algebraic number theory • Development • elliptic function • elliptic functions • Elliptische Funktion • Equation • ETCH • Form • Function • History of Mathematics • lattice • Mathematics • Number Theory • Outlook • Society • Story
ISBN-10	3-540-65036-9 / 3540650369
ISBN-13	978-3-540-65036-2 / 9783540650362
Zustand	Neuware