Elliptic Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Functions write by Serge Lang. This book was released on 2012-12-06. Elliptic Functions available in PDF, EPUB and Kindle. Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.
Elliptic Functions
Elliptic Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Functions write by Komaravolu Chandrasekharan. This book was released on 2012-12-06. Elliptic Functions available in PDF, EPUB and Kindle. This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.
Elliptic Functions According to Eisenstein and Kronecker
Elliptic Functions According to Eisenstein and Kronecker - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Functions According to Eisenstein and Kronecker write by Andre Weil. This book was released on 1999. Elliptic Functions According to Eisenstein and Kronecker available in PDF, EPUB and Kindle. 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 (...).
Elliptic Functions
Elliptic Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Functions write by Arthur Latham Baker. This book was released on 1890. Elliptic Functions available in PDF, EPUB and Kindle.
Lectures on Selected Topics in Mathematical Physics
Lectures on Selected Topics in Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Selected Topics in Mathematical Physics write by William A. Schwalm. This book was released on 2015-12-31. Lectures on Selected Topics in Mathematical Physics available in PDF, EPUB and Kindle. This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.
