Introduction to Elliptic Curves and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Elliptic Curves and Modular Forms write by Neal I. Koblitz. This book was released on 2012-12-06. Introduction to Elliptic Curves and Modular Forms available in PDF, EPUB and Kindle. The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Elliptic Curves, Modular Forms, and Their L-functions
Elliptic Curves, Modular Forms, and Their L-functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves, Modular Forms, and Their L-functions write by Álvaro Lozano-Robledo. This book was released on 2011. Elliptic Curves, Modular Forms, and Their L-functions available in PDF, EPUB and Kindle. 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.
LMSST: 24 Lectures on Elliptic Curves
LMSST: 24 Lectures on Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook LMSST: 24 Lectures on Elliptic Curves write by John William Scott Cassels. This book was released on 1991-11-21. LMSST: 24 Lectures on Elliptic Curves available in PDF, EPUB and Kindle. A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
A First Course in Modular Forms
A First Course in Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A First Course in Modular Forms write by Fred Diamond. This book was released on 2006-03-30. A First Course in Modular Forms available in PDF, EPUB and Kindle. This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
The 1-2-3 of Modular Forms
The 1-2-3 of Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The 1-2-3 of Modular Forms write by Jan Hendrik Bruinier. This book was released on 2008-02-10. The 1-2-3 of Modular Forms available in PDF, EPUB and Kindle. This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
