Number Theory and Related Fields, Jonathan M. Borwein; Igor Shparlinski; Wadim Zudil

Автор: Michael Rosen
Название: Number Theory in Function Fields
ISBN: 1441929541 ISBN-13(EAN): 9781441929549
Издательство: Springer
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Описание: Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con- sidering finite algebraic extensions K of Q, which are called algebraic num- ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.

Автор: Jonathan M. Borwein; Igor Shparlinski; Wadim Zudil
Название: Number Theory and Related Fields
ISBN: 1461466415 ISBN-13(EAN): 9781461466413
Издательство: Springer
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Цена: 13974.00 р.
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Описание: "Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia.

Автор: David Hilbert; F. Lemmermeyer; I.T. Adamson; N. Sc
Название: The Theory of Algebraic Number Fields
ISBN: 3642083064 ISBN-13(EAN): 9783642083068
Издательство: Springer
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Описание: Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is- chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati- cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.

Автор: Winfried Kohnen; Rainer Weissauer
Название: Conformal Field Theory, Automorphic Forms and Related Topics
ISBN: 3662438305 ISBN-13(EAN): 9783662438305
Издательство: Springer
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Цена: 23757.00 р.
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Описание: This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H.

Автор: Julien Barral; St?phane Seuret
Название: Recent Developments in Fractals and Related Fields
ISBN: 3319578030 ISBN-13(EAN): 9783319578033
Издательство: Springer
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Цена: 22359.00 р.
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Описание: Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing.

Автор: Winfried Kohnen; Rainer Weissauer
Название: Conformal Field Theory, Automorphic Forms and Related Topics
ISBN: 3662512505 ISBN-13(EAN): 9783662512500
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H.