Sinossi
The text grew out of lecture notes for a course Lozano-Robledo taught at an undergraduate summer school as part of the 2009 Park City Mathematics Institute. It is an introductory survey of the theory of elliptic curves, modular forms, and their Lfunctions, emphasizing examples rather than proofs. His goal is to provide a big picture of the surprising connections among these three types of mathematical objects, which seem so distinct. One theme is the statement of the modularity theorem (nee Taniyuama-Shimura-Weil conjecture), and one of its most renowned consequences, Fermat's last theorem. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
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Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library) (Student Mathematical Library, 58)
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American Mathematical Society, 2011
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Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library)
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Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library) (Student Mathematical Library, 58)
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Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library)
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Condizione: New. An introductory survey of elliptic curves, modular forms, and $L$-functions. The 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. Series: Student Mathematical Library. Num Pages: 195 pages, Illustrations. BIC Classification: PBMW. Category: (G) General (US: Trade). Dimension: 217 x 139 x 12. Weight in Grams: 266. . 2011. Paperback. . . . . Codice articolo V9780821852422
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Elliptic Curves, Modular Forms, and Their L-Functions
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Paperback. Condizione: New. 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, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. 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. Codice articolo LU-9780821852422
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Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library)
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American Mathematical Society, 2011
ISBN 10: 0821852426
ISBN 13: 9780821852422
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Condizione: New. An introductory survey of elliptic curves, modular forms, and $L$-functions. The 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. Series: Student Mathematical Library. Num Pages: 195 pages, Illustrations. BIC Classification: PBMW. Category: (G) General (US: Trade). Dimension: 217 x 139 x 12. Weight in Grams: 266. . 2011. Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9780821852422
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