Number Theory with an Emphasis on the Markoff Spectrum

Number Theory with an Emphasis on the Markoff Spectrum PDF Author: Andrew Pollington
Publisher: Routledge
ISBN: 135142775X
Category : Mathematics
Languages : en
Pages : 340

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Book Description
Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on: general problems of diophantine approximation; quadratic forms and their connections with automorphic forms; the modular group and its subgroups; continued fractions; hyperbolic geometry; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.

Number Theory with an Emphasis on the Markoff Spectrum

Number Theory with an Emphasis on the Markoff Spectrum PDF Author: Andrew Pollington
Publisher: Routledge
ISBN: 135142775X
Category : Mathematics
Languages : en
Pages : 340

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Book Description
Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on: general problems of diophantine approximation; quadratic forms and their connections with automorphic forms; the modular group and its subgroups; continued fractions; hyperbolic geometry; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.

The Markoff and Lagrange Spectra

The Markoff and Lagrange Spectra PDF Author: Thomas W. Cusick
Publisher: American Mathematical Soc.
ISBN: 0821815318
Category : Mathematics
Languages : en
Pages : 109

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Book Description
This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.

Number Theory

Number Theory PDF Author: Canadian Number Theory Association. Conference
Publisher: American Mathematical Soc.
ISBN: 9780821803127
Category : Mathematics
Languages : en
Pages : 460

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Book Description
This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.

Mathematical Constants

Mathematical Constants PDF Author: Steven R. Finch
Publisher: Cambridge University Press
ISBN: 9780521818056
Category : Mathematics
Languages : en
Pages : 634

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Book Description
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Number Theory

Number Theory PDF Author: W.A. Coppel
Publisher: Springer Science & Business Media
ISBN: 0387894853
Category : Mathematics
Languages : en
Pages : 620

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Book Description
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Additive Number Theory: Inverse Problems and the Geometry of Sumsets PDF Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 9780387946559
Category : Mathematics
Languages : en
Pages : 320

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Book Description
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

Approximation by Algebraic Numbers

Approximation by Algebraic Numbers PDF Author: Yann Bugeaud
Publisher: Cambridge University Press
ISBN: 1139455672
Category : Mathematics
Languages : en
Pages : 292

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Book Description
An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.

Analytic Number Theory:The Halberstam Festschrift 2

Analytic Number Theory:The Halberstam Festschrift 2 PDF Author: Bruce C. Berndt
Publisher: Springer Science & Business Media
ISBN: 9780817639334
Category : Mathematics
Languages : en
Pages : 464

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Book Description
The second of two volumes presenting papers from an international conference on analytic number theory. The two volumes contain 50 papers, with an emphasis on topics such as sieves, related combinatorial aspects, multiplicative number theory, additive number theory, and Riemann zeta-function.

Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis

Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis PDF Author: Hugh L. Montgomery
Publisher: American Mathematical Soc.
ISBN: 1470424444
Category : Education
Languages : en
Pages : 242

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Book Description
This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in nu.

Number Theory and Its Applications

Number Theory and Its Applications PDF Author: Cem Y. Yildrim
Publisher: CRC Press
ISBN: 1000673138
Category : Mathematics
Languages : en
Pages : 368

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Book Description
This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.