number theory volume ii analytic and modern tools 240 graduate texts in mathematics

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Number Theory

Author : Henri Cohen
ISBN : 9780387498942
Genre : Mathematics
File Size : 43. 52 MB
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This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.

Mathematics In The 21st Century

Author : Pierre Cartier
ISBN : 9783034808590
Genre : Mathematics
File Size : 30. 21 MB
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Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.

Open Problems In Mathematics

Author : John Forbes Nash, Jr.
ISBN : 9783319321622
Genre : Mathematics
File Size : 82. 32 MB
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The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Zeta Functions Over Zeros Of Zeta Functions

Author : André Voros
ISBN : 3642052037
Genre : Mathematics
File Size : 57. 49 MB
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In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.

Multiple Zeta Functions Multiple Polylogarithms And Their Special Values

Author : Jianqiang Zhao
ISBN : 9789814689410
Genre : Mathematics
File Size : 55. 79 MB
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This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research. The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter. Contents:Multiple Zeta FunctionsMultiple Polylogarithms (MPLs)Multiple Zeta Values (MZVs)Drinfeld Associator and Single-Valued MZVsMultiple Zeta Value IdentitiesSymmetrized Multiple Zeta Values (SMZVs)Multiple Harmonic Sums (MHSs) and Alternating VersionFinite Multiple Zeta Values and Finite Euler Sumsq-Analogs of Multiple Harmonic (Star) Sums Readership: Advanced undergraduates and graduate students in mathematics, mathematicians interested in multiple zeta values. Key Features:For the first time, a detailed explanation of the theory of multiple zeta values is given in book form along with numerous illustrations in explicit examplesThe book provides for the first time a comprehensive introduction to multiple polylogarithms and their special values at roots of unity, from the basic definitions to the more advanced topics in current active researchThe book contains a few quite intriguing results relating the special values of multiple zeta functions and multiple polylogarithms to other branches of mathematics and physics, such as knot theory and the theory of motivesMany exercises contain supplementary materials which deepens the reader's understanding of the main text

Automorphe Formen

Author : Anton Deitmar
ISBN : 9783642123900
Genre : Mathematics
File Size : 62. 77 MB
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Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.


Author : Helmut Koch
ISBN : 9783322803122
Genre : Mathematics
File Size : 70. 14 MB
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Hauptziel des Buches ist die Vermittlung des Grundbestandes der Algebraischen Zahlentheorie einschließlich der Theorie der normalen Erweiterungen bis hin zu einem Ausblick auf die Klassenkörpertheorie. Gleichberechtigt mit algebraischen Zahlen werden auch algebraische Funktionen behandelt. Dies geschieht einerseits um die Analogie zwischen Zahl- und Funktionenkörpern aufzuzeigen, die besonders deutlich im Falle eines endlichen Konstantenkörpers ist. Andererseits erhält man auf diese Weise eine Einführung in die Theorie der "höheren Kongruenzen" als eines wesentlichen Bestandteils der "Arithmetischen Geometrie". Obgleich das Buch hauptsächlich algebraischen Methoden gewidmet ist, findet man in der Einleitung auch einen kurzen Beweis des Primzahlsatzes nach Newman. In den Kapiteln 7 und 8 wird die Theorie der Heckeschen L-Reihen behandelt einschließlich der Verteilung der Primideale algebraischer Zahlkörper in Kegeln.

Meine Zahlen Meine Freunde

Author : Paulo Ribenboim
ISBN : 9783540879572
Genre : Mathematics
File Size : 78. 46 MB
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Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

Scientific And Technical Books And Serials In Print 1989

Author : Bowker Editorial Staff
ISBN : 0835225550
Genre :
File Size : 22. 75 MB
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Elementare Zahlentheorie

Author : Edmund Landau
ISBN : 9780821836521
Genre : Mathematics
File Size : 37. 64 MB
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Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German.

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