Elliptic curves, modular forms, and their L-functions
Material type:
TextLanguage: English Series: Student mathematical library ; IAS/Park City mathematical subseries ; volume 58Publication details: Providence : American mathematical society, 2010 Description: xiv, 194p. : ill. ; 22 cmISBN: 9781470425937Subject(s): MATHEMATICS | ELLIPTIC CURVES | MODULAR FORMS | L-FUNCTIONDDC classification: 511.381 Online resources: Table of Contents | Reviews Summary: Many 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
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NISER LIBRARY | 511.381 LOZ-E (Browse shelf(Opens below)) | R (REFERENCE) | N216 | |
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NBHM Books
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SMS Library | 511.381 LOZ-E (Browse shelf(Opens below)) | Available | N421 |
Browsing NISER LIBRARY shelves Close shelf browser (Hides shelf browser)
| 511.381 LAN-I Introduction to modular forms | 511.381 LAN-I Introduction to modular forms | 511.381 LEH-D Discontinuous groups and automorphic functions | 511.381 LOZ-E Elliptic curves, modular forms, and their L-functions | 511.381 LOZ-E Elliptic curves modular forms and their l functions | 511.381 MUR-P Problems in the theory of modular forms | 511.381 MUR-P Problems in the theory of modular forms |
Includes bibliographical references (p. 189-192) and index.
Many 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.
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