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Category: Number Theory

Hardy Spaces on the Euclidean Space (Springer Monographs in by Akihito Uchiyama

By Akihito Uchiyama

Uchiyama's decomposition of BMO services is taken into account the "Mount Everest of Hardy house theory". This publication is predicated at the draft, which the writer accomplished sooner than his unexpected loss of life in 1997. these days, his contributions are tremendous influential in quite a few fields of study, resulting in additional breakthroughs.

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Prime Obsession: Bernhard Riemann and the Greatest Unsolved by John Derbyshire

By John Derbyshire

In August 1859 Bernhard Riemann, a little-known 32-year previous mathematician, awarded a paper to the Berlin Academy titled: "On the variety of best Numbers below a Given Quantity." in the midst of that paper, Riemann made an incidental comment — a wager, a speculation. What he tossed out to the assembled mathematicians that day has confirmed to be nearly cruelly compelling to numerous students within the resulting years. this present day, after a hundred and fifty years of cautious learn and exhaustive learn, the query is still. Is the speculation precise or false?

Riemann's simple inquiry, the first subject of his paper, involved a simple yet however very important topic of mathematics — defining an actual formulation to trace and determine the prevalence of leading numbers. however it is that incidental comment — the Riemann speculation — that's the really awesome legacy of his 1859 paper. simply because Riemann used to be in a position to see past the development of the primes to figure strains of whatever mysterious and mathematically dependent shrouded within the shadows — refined adaptations within the distribution of these major numbers. significant for its readability, astonishing for its capability results, the speculation took on huge, immense value in arithmetic. certainly, the profitable way to this puzzle could bring in a revolution in major quantity concept. Proving or disproving it turned the best problem of the age.

It has turn into transparent that the Riemann speculation, whose answer turns out to hold tantalizingly simply past our seize, holds the foremost to quite a few medical and mathematical investigations. The making and breaking of contemporary codes, which rely on the houses of the major numbers, have roots within the speculation. In a sequence of striking advancements throughout the Seventies, it emerged that even the physics of the atomic nucleus is attached in methods no longer but totally understood to this unusual conundrum. removing the answer to the Riemann speculation has turn into an obsession for plenty of — the veritable "great white whale" of mathematical learn. but regardless of decided efforts via generations of mathematicians, the Riemann speculation defies resolution.

Alternating passages of terribly lucid mathematical exposition with chapters of elegantly composed biography and heritage, Prime Obsession is an interesting and fluent account of an epic mathematical secret that maintains to problem and excite the realm. Posited a century and a part in the past, the Riemann speculation is an highbrow dinner party for the cognoscenti and the curious alike. not only a narrative of numbers and calculations, Prime Obsession is the engrossing story of a constant hunt for an elusive facts — and people who were ate up via it.

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Automorphic Forms and Galois Representations: Volume 2 by Minhyong Kim,Fred Diamond,Payman L. Kassaei

By Minhyong Kim,Fred Diamond,Payman L. Kassaei

Automorphic varieties and Galois representations have performed a valuable function within the improvement of contemporary quantity idea, with the previous coming to prominence through the distinguished Langlands software and Wiles' facts of Fermat's final Theorem. This two-volume assortment arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic types and Galois Representations' in July 2011, the purpose of which was once to discover contemporary advancements during this sector. The expository articles and learn papers around the volumes mirror fresh curiosity in p-adic equipment in quantity idea and illustration concept, in addition to contemporary development on issues from anabelian geometry to p-adic Hodge idea and the Langlands application. the themes lined in quantity contain curves and vector bundles in p-adic Hodge concept, associators, Shimura types, the birational part conjecture, and different themes of up to date interest.

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Arithmetische Funktionen (German Edition) by Paul J. McCarthy,Markus Hablizel

By Paul J. McCarthy,Markus Hablizel

Dieses Buch bietet eine Einführung in die Theorie der arithmetischen Funktionen, welche zu den klassischen und dynamischen Gebieten der Zahlentheorie gehört.
Das Buch enthält breitgefächerte Resultate, die für alle mit den Grundlagen der Zahlentheorie vertrauten Leser zugänglich sind. Der Inhalt geht weit über das Spektrum hinaus, mit dem die meisten Lehrbücher dieses Thema behandeln. Intensiv besprochen werden beispielsweise Ramanujan-Summen, Fourier-Zerlegungen arithmetischer Funktionen, Anzahl der Lösungen von Kongruenzen, Dirichlet-Reihen und verallgemeinerte Dirichlet-Faltungen sowie arithmetische Funktionen auf Gittern.
Desweiteren sind viele bibliografische Anmerkungen sowie Verweise auf Originalliteratur aufgeführt. Mehr als four hundred Übungsaufgaben bilden darüber hinaus einen wesentlichen Bestandteil für die Erschließung des Themas.

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The Congruences of a Finite Lattice: A Proof-by-Picture by George Grätzer

By George Grätzer

Self-contained exposition presents the key effects on congruence lattices of finite lattices

Includes the newest findings from a pioneering researcher within the field

Features the author's signature "Proof-by-Picture" strategy and its conversion to transparencies

Contains entire proofs, an in depth bibliography and index, and approximately eighty open problems

Excellent grad textual content and reference

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Algebra (Springer-Lehrbuch) (German Edition) by Jens Carsten Jantzen,Joachim Schwermer

By Jens Carsten Jantzen,Joachim Schwermer

Ausgehend von einer grundlegenden Einführung in Begriffe und Methoden der Algebra werden im Buch die wesentlichen Ergebnisse dargestellt und ein Einblick in viele Entwicklungen innerhalb der Algebra gegeben, die mit anderen Gebieten der Mathematik stark verflochten sind.

 Beginnend mit Begriffsbildungen wie Gruppe und Ring führt das Buch hin zu den Körpererweiterungen und der Galoistheorie. Danach werden zentrale Teile der Theorie der Moduln, Algebren und Ringe behandelt. Die Theorie der Divisionsalgebren und ihre Klassifikation mit Hilfe der Brauergruppe werden entwickelt. Es schließen sich Einführungen in die algebraischen Zahlentheorie und die Theorie der quadratischen Formen an.

 In zahlreichen Supplementen findet guy Ausblicke auf weiterführende Themen. Betrachtet werden zum Beispiel allgemeine lineare Gruppen, Schiefpolynomringe, Darstellungen, Erweiterungen von Moduln, projektive Moduln und Frobenius-Algebren.

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Number Theory: An Introduction to Mathematics (Universitext) by W.A. Coppel

By W.A. Coppel

Number thought is greater than a finished remedy of the topic. it's an advent to issues in larger point arithmetic, and certain in its scope; issues from research, glossy algebra, and discrete arithmetic are all included.

The publication is divided into parts. Part A covers key innovations of quantity concept and will function a primary direction at the topic. half B delves into extra complicated issues and an exploration of comparable arithmetic. the necessities for this self-contained textual content are components from linear algebra. precious references for the reader are amassed on the finish of every bankruptcy. it really is appropriate as an advent to raised point arithmetic for undergraduates, or for self-study.

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Number Theory Arising From Finite Fields: Analytic And by John Knopfmacher,Wen-Bin Zhang

By John Knopfmacher,Wen-Bin Zhang

"Number conception bobbing up from Finite Fields: Analytic and Probabilistic thought" bargains a dialogue of the advances and advancements within the box of quantity idea bobbing up from finite fields. It emphasizes mean-value theorems of multiplicative capabilities, the speculation of additive formulations, and the traditional distribution of values from additive services. The paintings explores calculations from classical phases to rising discoveries in replacement summary major quantity theorems.

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Problem-Solving and Selected Topics in Number Theory: In the by Michael Th. Rassias

By Michael Th. Rassias

The booklet presents a self-contained advent to classical Number thought. all of the proofs of the person theorems and the options of the workouts are being offered step-by-step. a few ancient feedback also are offered. The booklet could be directed to complicated undergraduate, starting graduate scholars in addition to to scholars who arrange for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

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Fractal Zeta Functions and Fractal Drums: Higher-Dimensional by Michel L. Lapidus,Goran Radunović,Darko Žubrinić

By Michel L. Lapidus,Goran Radunović,Darko Žubrinić

This monograph offers a state of the art and obtainable remedy of a brand new common higher-dimensional conception of complicated dimensions, legitimate for arbitrary bounded subsets of Euclidean areas, in addition to for his or her typical generalization, relative fractal drums. It offers an important extension of the prevailing thought of zeta features for fractal strings to fractal units and arbitrary bounded units in Euclidean areas of any measurement. new periods of fractal zeta capabilities are brought, particularly, the space and tube zeta capabilities of bounded units, and their key homes are investigated. the idea is constructed step by step at a sluggish speed, and each step is definitely prompted by means of a variety of examples, historic comments and reviews, bearing on the gadgets lower than research to different techniques. detailed emphasis is put on the research of complicated dimensions of bounded units and their connections with the notions of Minkowski content material and Minkowski measurability, in addition to on fractal tube formulation. it's proven for the 1st time that crucial singularities of fractal zeta capabilities can obviously emerge for numerous periods of fractal units and feature an important geometric impression. the idea built during this booklet leads obviously to a brand new definition of fractality, expressed when it comes to the life of underlying geometric oscillations or, equivalently, by way of the life of nonreal complicated dimensions.  
The connections to earlier broad paintings of the 1st writer and his collaborators on geometric zeta features of fractal strings are basically defined. Many innovations are mentioned for the 1st time, making the publication a wealthy resource of recent techniques and ideas to be constructed extra. The ebook encompasses a huge variety of open difficulties and describes many attainable instructions for extra study. the start chapters can be used as part of a path on fractal geometry. the first readership is aimed toward graduate scholars and researchers operating in Fractal Geometry and different similar fields, resembling advanced research, Dynamical structures, Geometric degree thought, Harmonic research, Mathematical Physics, Analytic quantity idea and the Spectral thought of Elliptic Differential Operators. The publication can be available to nonexperts and novices to the field.

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