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Author :
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (926 download)
Download or read book On Waring's Problem for Cubes written by and published by . This book was released on 1950 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Timothy Charles Kenney
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (176 download)
Download or read book Waring's Problem for the Cases of Squares, Cubes, and Biquadrates written by Timothy Charles Kenney and published by . This book was released on 1976 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tim Browning
Publisher : Springer Nature
ISBN 13 : 3030868729
Total Pages : 175 pages
Book Rating : 4.0/5 (38 download)
Download or read book Cubic Forms and the Circle Method written by Tim Browning and published by Springer Nature. This book was released on 2021-11-19 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Author : R. C. Vaughan
Publisher : Cambridge University Press
ISBN 13 : 9780521234399
Total Pages : 184 pages
Book Rating : 4.2/5 (343 download)
Download or read book The Hardy-Littlewood Method written by R. C. Vaughan and published by Cambridge University Press. This book was released on 1981-07-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hardy-Littlewood method is a means of estimating the number of integer solutions of equations and was first applied to Waring's problem on representations of integers by sums of powers. This introduction to the method deals with its classical forms and outlines some of the more recent developments. Now in its second edition it has been fully updated; the author has made extensive revisions and added a new chapter to take account of major advances by Vaughan and Wooley. The reader is expected to be familiar with elementary number theory and postgraduate students should find it of great use as an advanced textbook. It will also be indispensable to all lecturers and research workers interested in number theory.
Author : K. F. Roth
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (1 download)
Download or read book 1. Proof that Almost All Positive Integers are Sums of a Square, a Positive Cube and a Fourth Power. 2. On Warings Problem for Cubes. 3. On the Difference Between Consecutive Square Free Numbers. 4. On a Problem of Heilbronn written by K. F. Roth and published by . This book was released on 1951 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.A. Bennett
Publisher : CRC Press
ISBN 13 : 0429611412
Total Pages : 458 pages
Book Rating : 4.4/5 (296 download)
Download or read book Number Theory for the Millennium III written by M.A. Bennett and published by CRC Press. This book was released on 2023-03-17 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.
Author : Jörg Brüdern
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (46 download)
Download or read book Sieves, the circle method, and waring's problem for cubes written by Jörg Brüdern and published by . This book was released on 1991 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kent D. Boklan
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Asymptotic Formula in Waring's Problem written by Kent D. Boklan and published by . This book was released on 1992 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
ISBN 13 : 1475738455
Total Pages : 350 pages
Book Rating : 4.4/5 (757 download)
Download or read book Additive Number Theory The Classical Bases written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.
Author : J. Brüdern
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (897 download)
Download or read book Sieves, the Circle Method, and Waring's Problem for Cubes written by J. Brüdern and published by . This book was released on 1991 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bruce Berndt
Publisher : CRC Press
ISBN 13 : 1000065286
Total Pages : 368 pages
Book Rating : 4.0/5 ( download)
Download or read book Surveys in Number Theory written by Bruce Berndt and published by CRC Press. This book was released on 2002-11-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research. It serves as an inspiration to graduate students and as a reference for research mathematicians.
Author : Edward Waring
Publisher : Legare Street Press
ISBN 13 : 9781019510810
Total Pages : 0 pages
Book Rating : 4.5/5 (18 download)
Download or read book Meditationes Algebraicae written by Edward Waring and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in 1770, this influential book on algebraic notation and computation laid the groundwork for modern symbolic algebra. The author introduces a new system of notation, including the use of symbols for constants and variables, and develops a series of algorithms for manipulating algebraic expressions. The book was highly regarded by mathematicians of the time and remains a classic work in the history of mathematics today. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author :
Publisher : Cambridge University Press
ISBN 13 : 0521573475
Total Pages : 248 pages
Book Rating : 4.5/5 (215 download)
Download or read book The Hardy-Littlewood Method written by and published by Cambridge University Press. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 0387266771
Total Pages : 455 pages
Book Rating : 4.3/5 (872 download)
Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Author : Ellina Grigorieva
Publisher : Birkhäuser
ISBN 13 : 3319909150
Total Pages : 405 pages
Book Rating : 4.3/5 (199 download)
Download or read book Methods of Solving Number Theory Problems written by Ellina Grigorieva and published by Birkhäuser. This book was released on 2018-07-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores the representations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
Author : Luogeng Hua
Publisher : American Mathematical Soc.
ISBN 13 : 0821849425
Total Pages : 206 pages
Book Rating : 4.8/5 (218 download)
Download or read book Additive Theory of Prime Numbers written by Luogeng Hua and published by American Mathematical Soc.. This book was released on 2009-12-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Author : Taekyun Kim
Publisher : MDPI
ISBN 13 : 3036503609
Total Pages : 206 pages
Book Rating : 4.0/5 (365 download)
Download or read book Current Trends in Symmetric Polynomials with Their Applications Ⅱ written by Taekyun Kim and published by MDPI. This book was released on 2021-03-19 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.
