000			03181nam a22002897a 4500
003			OSt
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008			160315b xxu||||| |||| 00| 0 eng d
020			_a9781470425937
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a511.381 _bLOZ-E
100			_aLozano-Robledo, Alvaro
245			_aElliptic curves, modular forms, and their L-functions
260			_aProvidence : _bAmerican mathematical society, _c2010
300			_axiv, 194p. : _bill. ; _c22 cm.
490			_aStudent mathematical library ; _aIAS/Park City mathematical subseries _vvolume 58
504			_aIncludes bibliographical references (p. 189-192) and index.
520			_aMany problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and L-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, 3344161/747348, and 2244035177043369699245575130906674863160948472041/8912332268928859588025535178967163570016480830. The theories of elliptic curves, modular forms, and L-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.
650			_aMATHEMATICS
650			_aELLIPTIC CURVES
650			_aMODULAR FORMS
650			_aL-FUNCTION
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-58-toc.pdf?_gl=1*gbm1tp*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTQ2NDk2MC41LjEuMTcxOTQ3MTUxOS4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/14996775-elliptic-curves-modular-forms-and-their-l-functions-student-mathemati?from_search=true&from_srp=true&qid=4RceLwDuh1&rank=1#CommunityReviews
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