Application to Dirichlet Series of Maximal Large Sieve Inequality
Author | : Jui-lin Lung |
Publisher | : |
Total Pages | : 10 |
Release | : 1990 |
Genre | : Dirichlet series |
ISBN | : |
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Author | : Jui-lin Lung |
Publisher | : |
Total Pages | : 10 |
Release | : 1990 |
Genre | : Dirichlet series |
ISBN | : |
Author | : Oliver Ramaré |
Publisher | : Springer |
Total Pages | : 199 |
Release | : 2009-01-15 |
Genre | : Mathematics |
ISBN | : 9386279401 |
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 | : Cem Y. Yildrim |
Publisher | : CRC Press |
Total Pages | : 364 |
Release | : 2020-03-06 |
Genre | : Mathematics |
ISBN | : 1000657418 |
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.
Author | : M. N. Huxley |
Publisher | : Clarendon Press |
Total Pages | : 510 |
Release | : 1996-06-13 |
Genre | : Mathematics |
ISBN | : 0191590320 |
In analytic number theory a large number of problems can be "reduced" to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput's method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background.
Author | : S. Mandelbrojt |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 1972 |
Genre | : Mathematics |
ISBN | : |
It is not our intention to present a treatise on Dirichlet series. This part of harmonic analysis is so vast, so rich in publications and in 'theorems' that it appears to us inconceivable and, to our mind, void of interest to assemble anything but a restricted (but relatively complete) branch of the theory. We have not tried to give an account of the very important results of G. P6lya which link his notion of maximum density to the analytic continuation of the series, nor the researches to which the names of A. Ostrowski and V. Bernstein are intimately attached. The excellent book of the latter, which was published in the Collection Borel more than thirty years ago, gives an account of them with all the clarity one can wish for. Nevertheless, some scattered results proved by these authors have found their place among the relevant results, partly by their statements, partly as a working tool. We have adopted a more personal point of view, in explaining the methods and the principles (as the title of the book indicates) that originate in our research work and provide a collection of results which we develop here; we have also included others, due to present-day authors, which enable us to form a coherent whole.
Author | : Peter D. T. A. Elliott |
Publisher | : Cambridge University Press |
Total Pages | : 368 |
Release | : 1997-02-13 |
Genre | : Mathematics |
ISBN | : 0521560888 |
Deals with analytic number theory; many new results.
Author | : G. Tenenbaum |
Publisher | : Cambridge University Press |
Total Pages | : 180 |
Release | : 1995-06-30 |
Genre | : Mathematics |
ISBN | : 9780521412612 |
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.