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Trigonometric Sums And Their Applications
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Book Synopsis Trigonometric Sums and Their Applications by : Andrei Raigorodskii
Download or read book Trigonometric Sums and Their Applications written by Andrei Raigorodskii and published by Springer Nature. This book was released on 2020-03-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.
Book Synopsis Trigonometric Sums in Number Theory and Analysis by : Gennady I. Arkhipov
Download or read book Trigonometric Sums in Number Theory and Analysis written by Gennady I. Arkhipov and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov ́s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.
Book Synopsis Exponential Sums and their Applications by : N.M Korobov
Download or read book Exponential Sums and their Applications written by N.M Korobov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications. The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included. It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.
Book Synopsis TEORIJA ?ISEL, MATEMATI?ESKIJ ANALIZ I ICH PRILOENIJA by : Ivan Matveevich Vinogradov
Download or read book TEORIJA ?ISEL, MATEMATI?ESKIJ ANALIZ I ICH PRILOENIJA written by Ivan Matveevich Vinogradov and published by American Mathematical Soc.. This book was released on 1983 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth by :
Download or read book Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth written by and published by American Mathematical Soc.. This book was released on 1973 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A two volume collection of mathematical papers on algebra and mathematics in honor of famed Russian mathematician, I.M. Vinogradov.
Book Synopsis Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis by : Helmut Maier
Download or read book Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis written by Helmut Maier and published by World Scientific. This book was released on 2021-12-28 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums — which constitute a very classical domain of research in Number Theory — as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretèche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Number Theoretic Methods by : Shigeru Kanemitsu
Download or read book Number Theoretic Methods written by Shigeru Kanemitsu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.
Book Synopsis Certain Number-Theoretic Episodes In Algebra, Second Edition by : R Sivaramakrishnan
Download or read book Certain Number-Theoretic Episodes In Algebra, Second Edition written by R Sivaramakrishnan and published by CRC Press. This book was released on 2019-03-19 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Book Synopsis The Riemann Zeta-Function by : Aleksandar Ivic
Download or read book The Riemann Zeta-Function written by Aleksandar Ivic and published by Courier Corporation. This book was released on 2012-07-12 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
Book Synopsis Analytic Number Theory by : Henryk Iwaniec
Download or read book Analytic Number Theory written by Henryk Iwaniec and published by American Mathematical Soc.. This book was released on 2021-10-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analytic Number Theory, Mathematical Anaylsis and Their Applications by : Sergeĭ Mikhaĭlovich Nikolʹskiĭ
Download or read book Analytic Number Theory, Mathematical Anaylsis and Their Applications written by Sergeĭ Mikhaĭlovich Nikolʹskiĭ and published by American Mathematical Soc.. This book was released on 1980 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: “The present collection of papers dedicated to Academician Ivan Matveevic Vinogradov on his eighty-fifth birthday, is a continuation of volume 142 in this series. The papers--original work on various chapter of number theory, analysis and also their applications—are of interest to specialists and graduate students in mathematics.” -- Title page verso.
Book Synopsis Droplets and Sprays by : Sergei Sazhin
Download or read book Droplets and Sprays written by Sergei Sazhin and published by Springer. This book was released on 2014-05-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a clear and systematic description of droplets and spray dynamic models, this book maximises reader insight into the underlying physics of the processes involved, outlines the development of new physical and mathematical models and broadens understanding of interactions between the complex physical processes which take place in sprays. Complementing approaches based on the direct application of computational fluid dynamics (CFD), Droplets and Sprays treats both theoretical and practical aspects of internal combustion engine process such as the direct injection of liquid fuel, subcritical heating and evaporation. Including case studies that illustrate the approaches relevance to automotive applications, it is also anticipated that the described models can find use in other areas such as in medicine and environmental science.
Book Synopsis 20 Lectures Delivered at the International Congress of Mathematicians in Vancouver, 1974 by :
Download or read book 20 Lectures Delivered at the International Congress of Mathematicians in Vancouver, 1974 written by and published by American Mathematical Soc.. This book was released on 1977-12-31 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiplicative Number Theory I by : Hugh L. Montgomery
Download or read book Multiplicative Number Theory I written by Hugh L. Montgomery and published by Cambridge University Press. This book was released on 2007 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt:
