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

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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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: Jonathan M. Borwein; Igor Shparlinski; Wadim Zudil
Название: Number Theory and Related Fields
ISBN: 1493902172 ISBN-13(EAN): 9781493902170
Издательство: Springer
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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: 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: 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.

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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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: Harald Niederreiter; Arne Winterhof
Название: Applied Number Theory
ISBN: 3319368125 ISBN-13(EAN): 9783319368122
Издательство: Springer
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Описание: This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory.

Автор: Henri Cohen
Название: A Course in Computational Algebraic Number Theory
ISBN: 3642081428 ISBN-13(EAN): 9783642081422
Издательство: Springer
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Описание: With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.

Автор: Carl Pomerance; Michael Th. Rassias
Название: Analytic Number Theory
ISBN: 3319355511 ISBN-13(EAN): 9783319355511
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Описание: This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field.

Автор: Krishnaswami Alladi
Название: Number Theory, Madras 1987
ISBN: 354051595X ISBN-13(EAN): 9783540515951
Издательство: Springer
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Автор: George Greaves
Название: Sieves in Number Theory
ISBN: 3642074952 ISBN-13(EAN): 9783642074950
Издательство: Springer
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Описание: Slightly more than 25 years ago, the first text devoted entirely to sieve meth- ods made its appearance, rapidly to become a standard source and reference in the subject. The book of H. Halberstam and H.-E. Richert had actually been conceived in the mid-1960's. The initial stimulus had been provided by the paper of W. B. Jurkat and Richert, which determined the sifting limit for the linear sieve, using a combination of the, A2 method of A. Selberg with combinatorial ideas which were in themselves of great importance and in- terest. One of the declared objectives in writing their book was to place on record the sharpest form of what they called Selberg sieve theory available at the time. At the same time combinatorial methods were not neglected, and Halber- stam and Richert included an account of the purely combinatorial method of Brun, which they believed to be worthy of further examination. Necessar- ily they included only a briefer mention of the development of these ideas due (independently) to J. B. Rosser and H. Iwaniec that became generally available around 1971. These combinatorial notions have played a central part in subsequent developments, most notably in the papers of Iwaniec, and a further account may be thought to be timely. There have also been some developments in the theory of the so-called sieve with weights, and an account of these will also be included in this book.

Автор: H. Jager
Название: Number Theory, Noordwijkerhout 1983
ISBN: 3540133569 ISBN-13(EAN): 9783540133568
Издательство: Springer
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