Lectures on the Theory of Elliptic Modular Functions: First Volume, Felix Klein, Robert Fricke
Автор: Felix Klein, Robert Fricke Название: Lectures on the Theory of Automorphic Functions: First Volume ISBN: 7040478404 ISBN-13(EAN): 9787040478402 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 88710.00 T Наличие на складе: Невозможна поставка. Описание: Felix Klein's famous Erlangen program made the theory of group actions into a central part of mathematics. In the spirit of this program, Klein set out to write a grand series of books which unified many different subjects of mathematics, including number theory, geometry, complex analysis, and discrete subgroups. The first book on icosahedron and the solution of equations of the fifth degree showed closed relations between three seemingly different subjects: the symmetries of the icosahedron, the solution to fifth degree algebraic equations, and the differential equation of hypergeometric functions. It was translated into English in 1888, four years after its original German version was published in 1884. It was followed by two volumes on elliptic modular functions by Klein and Fricke and two more volumes on automorphic functions also by Klein and Fricke. These four classic books are vast generalizations of the first volume and contain the highly original works of Poincaré and Klein on automorphic forms. They have been very influential in the development of mathematics and are now available in English for the first time. These books contain many original ideas, striking examples, explicit computations, and details which are not available anywhere else. They will be very valuable references for people at all levels and allow the reader to see the unity of mathematics through the eyes of one of the most influential mathematicians with vision, Felix Klein.
Автор: Felix Klein, Robert Fricke Название: Lectures on the Theory of Automorphic Functions: Second Volume ISBN: 7040478390 ISBN-13(EAN): 9787040478396 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 88710.00 T Наличие на складе: Невозможна поставка. Описание: Felix Klein's famous Erlangen program made the theory of group actions into a central part of mathematics. In the spirit of this program, Klein set out to write a grand series of books which unified many different subjects of mathematics, including number theory, geometry, complex analysis, and discrete subgroups. The first book on icosahedron and the solution of equations of the fifth degree showed closed relations between three seemingly different subjects: the symmetries of the icosahedron, the solution to fifth degree algebraic equations, and the differential equation of hypergeometric functions. It was translated into English in 1888, four years after its original German version was published in 1884. It was followed by two volumes on elliptic modular functions by Klein and Fricke and two more volumes on automorphic functions also by Klein and Fricke. These four classic books are vast generalizations of the first volume and contain the highly original works of Poincaré and Klein on automorphic forms. They have been very influential in the development of mathematics and are now available in English for the first time. These books contain many original ideas, striking examples, explicit computations, and details which are not available anywhere else. They will be very valuable references for people at all levels and allow the reader to see the unity of mathematics through the eyes of one of the most influential mathematicians with vision, Felix Klein.
Автор: Felix Klein, Robert Fricke Название: Lectures on the Theory of Elliptic Modular Functions: Second Volume ISBN: 7040478374 ISBN-13(EAN): 9787040478372 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 88710.00 T Наличие на складе: Невозможна поставка. Описание: Felix Klein's famous Erlangen program made the theory of group actions into a central part of mathematics. In the spirit of this program, Klein set out to write a grand series of books which unified many different subjects of mathematics, including number theory, geometry, complex analysis, and discrete subgroups. The first book on icosahedron and the solution of equations of the fifth degree showed closed relations between three seemingly different subjects: the symmetries of the icosahedron, the solution to fifth degree algebraic equations, and the differential equation of hypergeometric functions. It was translated into English in 1888, four years after its original German version was published in 1884. It was followed by two volumes on elliptic modular functions by Klein and Fricke and two more volumes on automorphic functions also by Klein and Fricke. These four classic books are vast generalizations of the first volume and contain the highly original works of Poincaré and Klein on automorphic forms. They have been very influential in the development of mathematics and are now available in English for the first time. These books contain many original ideas, striking examples, explicit computations, and details which are not available anywhere else. They will be very valuable references for people at all levels and allow the reader to see the unity of mathematics through the eyes of one of the most influential mathematicians with vision, Felix Klein.
Автор: Roy Название: Elliptic and Modular Functions from Gauss to Dedekind to Hecke ISBN: 1107159385 ISBN-13(EAN): 9781107159389 Издательство: Cambridge Academ Рейтинг: Цена: 80250.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Many mathematicians today believe mathematical works from past centuries are inaccessible, not useful, or both. This book demonstrates that past works are not only readable, but brimming with ideas and insights. It is aimed at graduate students or researchers working in modular functions, number theory, complex analysis, or special functions.
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: 74970.00 T 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.
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: Kuyk Название: Modular Functions of One Variable I ISBN: 354006219X ISBN-13(EAN): 9783540062196 Издательство: Springer Рейтинг: Цена: 23250.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Willem Kuyk; J.-P. Serre Название: Modular Functions of One Variable III ISBN: 3540064834 ISBN-13(EAN): 9783540064831 Издательство: Springer Рейтинг: Цена: 37220.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: J.-P. Serre; D. B. Zagier Название: Modular Functions of One Variable VI ISBN: 3540085300 ISBN-13(EAN): 9783540085300 Издательство: Springer Рейтинг: Цена: 37220.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Tom M. Apostol Название: Modular Functions and Dirichlet Series in Number Theory ISBN: 1461269784 ISBN-13(EAN): 9781461269786 Издательство: Springer Рейтинг: Цена: 55890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function.
Автор: Berger Laurent Название: Elliptic Curves, Hilbert Modular Forms and Galois Deformatio ISBN: 3034806175 ISBN-13(EAN): 9783034806176 Издательство: Springer Рейтинг: Цена: 27940.00 T 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.
Название: Introduction to Elliptic Curves and Modular Forms ISBN: 1461269423 ISBN-13(EAN): 9781461269427 Издательство: Springer Рейтинг: Цена: 51200.00 T 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.
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