Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 106
Book Description
Galois Representations of Elliptic Curves and Abelian Entanglements
Author: Abelian l-Adic Representations and Elliptic Curves
Author: Jean-Pierre SerrePublisher: CRC Press
ISBN: 1439863865
Category : Mathematics
Languages : en
Pages : 203
Book Description
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Elliptic Curves and Big Galois Representations
Author: Daniel DelbourgoPublisher: Cambridge University Press
ISBN: 0521728665
Category : Mathematics
Languages : en
Pages : 283
Book Description
Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists.
Abelian L-adic Representations and Elliptic Curves
Author: Jean Pierre SerrePublisher:
ISBN: 9780805387254
Category :
Languages : en
Pages :
Book Description
LuCaNT: LMFDB, Computation, and Number Theory
Author: John CremonaPublisher: American Mathematical Soc.
ISBN: 1470472600
Category : Mathematics
Languages : en
Pages : 386
Book Description
This book will be published Open Access with a Creative Commons Attribution 4.0 International License (CC BY 4.0). The eBook can be downloaded electronically for free. This volume contains the proceedings of the LuCaNT (LMFDB, Computation, and Number Theory) conference held from July 10–14, 2023, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island and affiliated with Brown University. This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.
Elliptic Curves and Related Topics
Author: H. KisilevskyPublisher: American Mathematical Soc.
ISBN: 9780821870358
Category : Mathematics
Languages : en
Pages : 208
Book Description
This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.
Abelian P-adic Representations and Elliptic Curves
Author: Jean-Pierre SerreRational Points on Elliptic Curves
Author: Joseph H. SilvermanPublisher: Springer
ISBN: 3319185888
Category : Mathematics
Languages : en
Pages : 349
Book Description
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Abelian One-adic Representations and Elliptic Curves
Author: Jean Pierre SerrePublisher:
ISBN:
Category : Abelian groups
Languages : en
Pages :
Book Description
Elliptic Curves and Modular Forms
Author: Proceedings of the National Academy of SciencesPublisher: National Academies Press
ISBN: 9780309058759
Category : Reference
Languages : en
Pages : 52
Book Description