p-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz

Автор: Neal Koblitz
Название: p-adic Numbers, p-adic Analysis, and Zeta-Functions
ISBN: 1461270146 ISBN-13(EAN): 9781461270140
Издательство: Springer
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Описание: This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-function, plus new exercises and an appendix of answers and hints.

Автор: Arakawa Tsuneo
Название: Bernoulli Numbers and Zeta Functions
ISBN: 4431549188 ISBN-13(EAN): 9784431549185
Издательство: Springer
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Описание: The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. a formula for Bernoulli numbers by Stirling numbers; congruences between some class numbers and Bernoulli numbers;

Автор: Escassut Alain
Название: Value Distribution In P-Adic Analysis
ISBN: 9814730106 ISBN-13(EAN): 9789814730105
Издательство: World Scientific Publishing
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Описание:

The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.

Автор: Alain M. Robert
Название: A Course in p-adic Analysis
ISBN: 0387986693 ISBN-13(EAN): 9780387986692
Издательство: Springer
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Описание: It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel`s functional equation lemma, and a treatment of analytic elements.

Автор: Francesco Baldassari; Siegfried Bosch; Bernard Dwo
Название: p-adic Analysis
ISBN: 3540534776 ISBN-13(EAN): 9783540534778
Издательство: Springer
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Цена: 5583.00 р.
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Описание: Dedicated to Philippe Robba, this conference was characterized by the discussion of numerous algebraic geometries. Other papers were devoted to exponential sums, a theme connecting p-adic analysis to number theory.

Автор: Gan Wee Teck, Tan Kai Meng
Название: Modular Representation Theory of Finite and P-Adic Groups
ISBN: 981465180X ISBN-13(EAN): 9789814651806
Издательство: World Scientific Publishing
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Описание: This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013.

Автор: Hida, Haruzo
Название: P-adic automorphic forms on shimura varieties
ISBN: 1441919236 ISBN-13(EAN): 9781441919236
Издательство: Springer
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Описание: In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon- ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de- pending on their weights, and this book is the outgrowth of the lectures given there.

Автор: Tsuneo Arakawa; Tomoyoshi Ibukiyama; Masanobu Kane
Название: Bernoulli Numbers and Zeta Functions
ISBN: 4431563830 ISBN-13(EAN): 9784431563839
Издательство: Springer
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Описание: The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. a formula for Bernoulli numbers by Stirling numbers; congruences between some class numbers and Bernoulli numbers;

Автор: C. J. Bushnell; A. Fr?hlich
Название: Gauss Sums and p-adic Division Algebras
ISBN: 3540122907 ISBN-13(EAN): 9783540122906
Издательство: Springer
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