Elliptic Curves, Modular Forms and Iwasawa Theory, David Loeffler; Sarah Livia Zerbes
Название: Introduction to Elliptic Curves and Modular Forms ISBN: 1461269423 ISBN-13(EAN): 9781461269427 Издательство: Springer Рейтинг: Цена: 7680.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Ash Avner, Gross Robert Название: Elliptic Tales: Curves, Counting, and Number Theory ISBN: 0691163502 ISBN-13(EAN): 9780691163505 Издательство: Wiley Рейтинг: Цена: 2216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture
Автор: Silverman Joseph H. Название: Arithmetic of Elliptic Curves ISBN: 1441918582 ISBN-13(EAN): 9781441918581 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields.
Автор: Thanasis Bouganis; Otmar Venjakob Название: Iwasawa Theory 2012 ISBN: 3662512211 ISBN-13(EAN): 9783662512210 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Lecture notes: C. Wuthrich: Overview of some Iwasawa theory.- X. Wan: Introduction to Skinner-Urban's Work on the Iwasawa Main Conjecture for GL₂.- Research and Survey articles: D. Benois: On extra zeros of p-adic L-functions: The crystalline case.- Th. Bouganis: On Special L-values attached to Siegel modular forms.- T. Fukaya et al: Modular symbols in Iwasawa theory.- T. Fukuda et al: Weber's class number one problem.- R. Greenberg: On p-adic Artin L-functions II.- M.-L. Hsieh: Iwasawa μ-invariants of p-adic Hecke L-functions.- S. Kobayashi: The p-adic height pairing on abelian varieties at non-ordinary primes.- J. Kohlhaase: Iwasawa modules arising from deformation spaces of p-divisible formal group laws.- M. Kurihara: The structure of Selmer groups for elliptic curves and modular symbols.- D. Loeffler: P-adic integration on ray class groups and non-ordinary p-adic L-functions.- T. Nguyen Quang Do: On equivariant characteristic ideals of real classes.- E. Urban: Nearly over convergent modular forms.- M. Witte: Non commutative L-functions for varieties over finite fields.- Z. Wojtkowiak: On $\widehat{\mathbb{Z}}$-zeta function.
Автор: Berger Laurent Название: Elliptic Curves, Hilbert Modular Forms and Galois Deformatio ISBN: 3034806175 ISBN-13(EAN): 9783034806176 Издательство: Springer Рейтинг: Цена: 4191.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book details recent developments and major changes in Galois deformation theory during the last decade, including deformations of pseudo-representations, framed deformations, and groupoids.
Автор: John Coates; Peter Schneider; R. Sujatha; Otmar Ve Название: Noncommutative Iwasawa Main Conjectures over Totally Real Fields ISBN: 3642443354 ISBN-13(EAN): 9783642443350 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.
Автор: Haruzo Hida Название: Elliptic Curves and Arithmetic Invariants ISBN: 1489990925 ISBN-13(EAN): 9781489990921 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.
Автор: Joseph H. Silverman; John T. Tate Название: Rational Points on Elliptic Curves ISBN: 3319307576 ISBN-13(EAN): 9783319307572 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Introduction.- Geometry and Arithmetic.- Points of Finite Order.- The Group of Rational Points.- Cubic Curves over Finite Fields.- Integer Points on Cubic Curves.- Complex Multiplication.
Автор: Haruzo Hida Название: Elliptic Curves and Arithmetic Invariants ISBN: 1461466563 ISBN-13(EAN): 9781461466567 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.
The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi's elliptic function approach dates from his epic Fundamenta Nova of 1829. Here, the author employs his combinatorial/elliptic function methods to derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi's (1829) 4 and 8 squares identities to 4n2 or 4n(n+1) squares, respectively, without using cusp forms such as those of Glaisher or Ramanujan for 16 and 24 squares. These results depend upon new expansions for powers of various products of classical theta functions. This is the first time that infinite families of non-trivial exact explicit formulas for sums of squares have been found.
The author derives his formulas by utilizing combinatorics to combine a variety of methods and observations from the theory of Jacobi elliptic functions, continued fractions, Hankel or Turanian determinants, Lie algebras, Schur functions, and multiple basic hypergeometric series related to the classical groups. His results (in Theorem 5.19) generalize to separate infinite families each of the 21 of Jacobi's explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical theta functions in sections 40-42 of the Fundamental Nova. The author also uses a special case of his methods to give a derivation proof of the two Kac and Wakimoto (1994) conjectured identities concerning representations of a positive integer by sums of 4n2 or 4n(n+1) triangular numbers, respectively. These conjectures arose in the study of Lie algebras and have also recently been proved by Zagier using modular forms. George Andrews says in a preface of this book, This impressive work will undoubtedly spur others both in elliptic functions and in modular forms to build on these wonderful discoveries.'
Audience: This research monograph on sums of squares is distinguished by its diversity of methods and extensive bibliography. It contains both detailed proofs and numerous explicit examples of the theory. This readable work will appeal to both students and researchers in number theory, combinatorics, special functions, classical analysis, approximation theory, and mathematical physics.
Автор: Cooper Shaun Et Al Название: Development Of Elliptic Functions According To Ramanujan ISBN: 9814366455 ISBN-13(EAN): 9789814366458 Издательство: World Scientific Publishing Рейтинг: Цена: 11246.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Provides an efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. This book is suitable for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan`s work.
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