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Author: Seppo Pajunen
Publisher:
ISBN: 9789517205207
Category :
Languages : en
Pages :
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Book Description
Author: Seppo Pajunen
Publisher:
ISBN: 9789517205207
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: E. Kowalski
Publisher: Cambridge University Press
ISBN: 9780521888516
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
Author: E. Kowalski
Publisher: Cambridge University Press
ISBN: 1139472976
Category : Mathematics
Languages : en
Pages :
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Book Description
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
Author: Emmanuel Kowalski
Publisher:
ISBN: 9780511398063
Category : Arithmetical algebraic geometry
Languages : en
Pages : 293
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Book Description
Author: Alina Carmen Cojocaru
Publisher: Cambridge University Press
ISBN: 9780521848169
Category : Mathematics
Languages : en
Pages : 250
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Book Description
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.
Author: Heine Halberstam
Publisher: Courier Corporation
ISBN: 0486320804
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.
Author: Oliver Ramaré
Publisher: Springer
ISBN: 9386279401
Category : Mathematics
Languages : en
Pages : 199
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Book Description
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved.
Author: Henryk Iwaniec
Publisher: American Mathematical Soc.
ISBN: 1470467704
Category : Education
Languages : en
Pages : 615
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Book Description
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Author: David V. Chudnovsky
Publisher: Springer
ISBN: 3540466401
Category : Mathematics
Languages : en
Pages : 263
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Book Description
The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications. Papers included in this volume are based on the lectures presented by their authors at the Seminar at the Graduate Center of C.U.N.Y. in 1985-88. Papers in the volume cover a wide spectrum of number theoretic topics ranging from additive number theory and diophantine approximations to algebraic number theory and relations with algebraic geometry and topology.
Author: Yuan Wang
Publisher: World Scientific
ISBN: 9812381597
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This book provides a detailed description of a most important unsolved mathematical problem ? the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.
