An Introduction To Sieve Methods And Their Applications

Autor: Alina Carmen Cojocaru
Publisher: Cambridge University Press
ISBN: 9780521848169
File Size: 58,64 MB
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Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.

Clifford Algebras An Introduction

Autor: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 1107096383
File Size: 19,67 MB
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A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

A Course In Analytic Number Theory

Autor: Marius Overholt
Publisher: American Mathematical Soc.
ISBN: 1470417065
File Size: 17,78 MB
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This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

The Homotopy Theory Of 1 Categories

Autor: Julia E. Bergner
Publisher: Cambridge University Press
ISBN: 1107101360
File Size: 80,12 MB
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An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

Prime Detecting Sieves Lms 33

Autor: Glyn Harman
Publisher: Princeton University Press
ISBN: 1400845939
File Size: 54,98 MB
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This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.

The Geometry Of Celestial Mechanics

Autor: Hansjörg Geiges
Publisher: Cambridge University Press
ISBN: 1107125405
File Size: 51,92 MB
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A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.

Fourier Analysis With Applications

Autor: Adrian Constantin
Publisher: Cambridge University Press
ISBN: 1107044103
File Size: 79,81 MB
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Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.