Overview
"These notes constitute a lucid introduction to ""Elliptic Curves"", one of the central and vigorous areas of current mathematical research. The subject has been studied from diverse viewpoints --- analytic, algebraic and arithmetical; It offers the reader glimpses of all three aspects and presents some of the basic important theorems in all of them. The first part introduces a little of the theory of Riemann surfaces and goes on to the study of tori and their projective embeddings as cubics. This part ends with a discussion of the identification of the moduli space of complex tori with the quotient of the upper half plane by the modular groups. The second part handles the algebraic geometry of elliptic curves. It begins with a rapid introduction to some basic algebraic geometry and then focuses on elliptic curves. The Riemann-Roch theorem and the Riemann hypothesis for elliptic curves are proved and the structure of endomorphism ring of an elliptic curve are described. The third and last part is on the arithmetic of elliptic curves over $Q$. The Mordell-Weil theorem, Mazur's theorem on torsion in rational points of an elliptic curve over $Q$, theorems of Thue and Siegel are among the results which are presented. There is a brief discussion of theta functions, Eisenstein series and cusp forms with an application to representation of natural numbers as sums of squares. The notes end with the formulation of the Birch and Swinnerton-Dyer conjectures. There is an additional brief chapter (Appendix C) written in July 2004 by Kirti Joshi describing some developments."
Full Product Details
Author: R. V. Gurjar ,
Kirti Joshi ,
N. Mohan Kumar ,
et al.
Publisher: Narosa Publishing House
Imprint: Narosa Publishing House
ISBN: 9788173195020
ISBN 10: 8173195021
Pages: 370
Publication Date: 18 September 2006
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: Out of stock
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.
Author Information
Kapil H. Paranjape.: Department of Mathematics The Institute of Mathematical Sciences, C.I.T. Campus, Taramani Chennai - 600113, India T. N. Shorey.: School of Mathematics Tata Institute of Fundamental Research, Colaba, Mumbai - 400005, India R. R. Simha.: Retired Professor, School of Mathematics Tata Institute of Fundamental Research, Colaba, Mumbai - 400005, India V. Srinivas.: School of Mathematics Tata Institute of Fundamental Research, Colaba, Mumbai - 400005, India R. V. Gurjar.: School of Mathematics Tata Institute of Fundamental Research, Colaba, Mumbai - 400005, India Kirti Joshi.: Department of Mathematics, University of Arizona 617 N. Santa Rita Ave., P.O. Box 210089, Tueson, AZ 85721 - 0089, USA N. Mohan Kumar.: Department of Mathematics Washington University in St. Louis, St. Louis, Missouri - 63130, USA
