Elliptic Curves, Modular Forms, and Their L-functions 在线电子书 图书标签: 数学 美国 模形式 椭圆曲线 数论中三个非常重要的对象 数论 AG
发表于2024-12-23
Elliptic Curves, Modular Forms, and Their L-functions 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024
最有用的部分是介绍Sage的附录
评分一本薄书介绍三个大对象,必须是导引书,但导引的不错。
评分最有用的部分是介绍Sage的附录
评分一本薄书介绍三个大对象,必须是导引书,但导引的不错。
评分最有用的部分是介绍Sage的附录
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.
This book is published in cooperation with IAS/Park City Mathematics Institute.
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Elliptic Curves, Modular Forms, and Their L-functions 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024