Lectures on the Theory of Automorphic Functions: First Volume, Felix Klein, Robert Fricke

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)
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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: Paul Garrett
Название: Modern Analysis of Automorphic Forms By Example 2 Hardback Book Set
ISBN: 1108697933 ISBN-13(EAN): 9781108697934
Издательство: Cambridge Academ
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Описание: This two-volume book provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The featured critical results, which are proven carefully and in detail, include: discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem in Volume 1; and automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics in Volume 2. The book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

Автор: Stephen Gelbart; Ilya Piatetski-Shapiro; Stephen R
Название: Explicit Constructions of Automorphic L-Functions
ISBN: 3540178481 ISBN-13(EAN): 9783540178484
Издательство: Springer
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Описание: Intends to derive the analytic continuation and functional equation of the L-functions attached by R P Langlands to automorphic representations of reductive algebraic groups. This book deals with L-functions for the simple classical groups; and with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n.

Автор: A.B. Venkov
Название: Spectral Theory of Automorphic Functions
ISBN: 079230487X ISBN-13(EAN): 9780792304876
Издательство: Springer
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Описание: 'Et moi, ..., si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Автор: Goldfeld
Название: Automorphic Forms and L-Functions for the Group GL(n,R)
ISBN: 1107565022 ISBN-13(EAN): 9781107565029
Издательство: Cambridge Academ
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Описание: L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with basic knowledge of classical analysis, complex variable theory, and algebra.

Автор: Jan Hendrik Bruinier; Winfried Kohnen
Название: L-Functions and Automorphic Forms
ISBN: 3319697110 ISBN-13(EAN): 9783319697116
Издательство: Springer
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Описание: The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways.

Автор: Dihua Jiang, Freydoon Shahidi, David Soudry
Название: Advances in the Theory of Automorphic Forms and Their $L$-functions
ISBN: 147041709X ISBN-13(EAN): 9781470417093
Издательство: Mare Nostrum (Eurospan)
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Описание: This volume contains the proceedings of the workshop on ``Advances in the Theory of Automorphic Forms and Their $L$-functions'' held in honor of James Cogdell's 60th birthday, held from October 16-25, 2013, at the Erwin Schrodinger Institute (ESI) at the University of Vienna.The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their $L$-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of $p$-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, $L$-functions for classical groups, special values of $L$-functions, Howe duality, subconvexity for $L$-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on $L$-functions, nodal sets and geometry.

Автор: Diamond
Название: Automorphic Forms and Galois Representations
ISBN: 1107691923 ISBN-13(EAN): 9781107691926
Издательство: Cambridge Academ
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Описание: This collection, the first of two volumes arising from an LMS-EPSRC Durham Symposium, explores the importance of automorphic forms and Galois representations in number theory. The expository articles and research papers within cover recent progress in anabelian geometry, p-adic Hodge theory, the Langlands program, and p-adic methods in number theory.

Автор: Roelof Bruggeman, Youngju Choie, Nikolaos Diamantis
Название: Holomorphic Automorphic Forms and Cohomology
ISBN: 1470428555 ISBN-13(EAN): 9781470428556
Издательство: Mare Nostrum (Eurospan)
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Описание: Investigates the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least $2$ this correspondence is given by the Eichler integral. The authors use Knopp`s generalization of this integral to real weights, and apply it to complex weights that are not an integer at least $2$.

Автор: Bernhard Heim; Mehiddin Al-Baali; Tomoyoshi Ibukiy
Название: Automorphic Forms
ISBN: 3319363379 ISBN-13(EAN): 9783319363370
Издательство: Springer
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Описание: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "International Conference on Automorphic Forms and Number Theory," held in Muscat, Sultanate of Oman.

Автор: A.B. Venkov
Название: Spectral Theory of Automorphic Functions
ISBN: 9401073449 ISBN-13(EAN): 9789401073448
Издательство: Springer
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