Number theory Books
Cambridge University Press Elliptic Curves in Cryptography 265 London Mathematical Society Lecture Note Series Series Number 265
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£62.69
Cambridge University Press Automorphic Forms Representations 55 Cambridge Studies in Advanced Mathematics Series Number 55
Book SynopsisIntermediate in level between an advanced textbook and a monograph, this book covers both the classical and representation theoretic views of automorphic forms in a style which is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the RankinâSelberg method and the triple L-function, examining this subject matter from many different and complementary viewpoints. Researchers as well as students will find this a valuable guide to a notoriously difficult subject.Trade Review'This important textbook closes a gap in the existing literature, for it presents the 'representation theoretic' viewpoint of the theory of automorphic forms on GL(2) … it will become a stepping stone for many who want to study the Corvallis Proceedings or the Lecture Notes by H. Jaquet and R. Langlands or seek a pathway to R. Langland's conjectures.' Monatshefte für Mathematik'Students and researchers will find the book an understandable and penetrating treatment of a beautiful theory.' European Mathematical SocietyTable of Contents1. Modular forms; 2. Automorphic forms and representations of GL( 2, R); 3. Automorphic representations; 4. GL(2) over a p-adic field.
£56.99
Cambridge University Press Surveys in Geometry and Number Theory Reports on Contemporary Russian Mathematics 338 London Mathematical Society Lecture Note Series Series Number 338
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£74.13
Cambridge University Press LFunctions and Galois Representations 320 London Mathematical Society Lecture Note Series Series Number 320
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£88.21
Cambridge University Press Heights in Diophantine Geometry 4 New Mathematical Monographs Series Number 4
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£62.69
Cambridge University Press Number Theory and Polynomials London Mathematical Society Lecture Note Series Series Number 352
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£61.71
Cambridge University Press The Higher Arithmetic An Introduction to the
Book SynopsisNow into its eighth edition and with additional material on primality testing written by J. H. Davenport, The Higher Arithmetic introduces concepts and theorems in a way that does not assume an in-depth knowledge of the theory of numbers but touches upon matters of deep mathematical significance.Trade Review'Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer's opinion, is far superior for this purpose to any other book in English.' From a review of the first edition in Bulletin of the American Mathematical Society'… the well-known and charming introduction to number theory … can be recommended both for independent study and as a reference text for a general mathematical audience.' European Maths Society Journal'Its popularity is based on a very readable style of exposition.' EMS NewsletterTable of ContentsIntroduction; 1. Factorization and the primes; 2. Congruences; 3. Quadratic residues; 4. Continued fractions; 5. Sums of squares; 6. Quadratic forms; 7. Some Diophantine equations; 8. Computers and number theory; Exercises; Hints; Answers; Bibliography; Index; Additional notes.
£37.99
Cambridge University Press Elliptic Curves and Big Galois Representations London Mathematical Society Lecture Note Series Series Number 356
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£74.13
Cambridge University Press A Mathematical Tapestry
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£75.99
Cambridge University Press Complex Multiplication 15 New Mathematical Monographs Series Number 15
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£122.55
Cambridge University Press Modular Forms and Galois Cohomology 69 Cambridge Studies in Advanced Mathematics Series Number 69
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£122.55
Cambridge University Press Diffusions Markov Processes and Martingales Volume 2 Ito Calculus
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£66.49
Cambridge University Press Diffusions Markov Processes and Martingales Volume 1 Foundations Cambridge Mathematical Library
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£65.54
Cambridge University Press Special Functions 71 Encyclopedia of Mathematics and its Applications Series Number 71
Book SynopsisSpecial functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and applicaTrade Review'Occasionally there is published a mathematics book that one is compelled to describe as, well, let us say, special. Special Functions is certainly one of those rare books. … this treatise … should become a classic. Every student, user, and researcher in analysis will want to have it close at hand as she/he works.' The Mathematical Intelligencer' … the material is written in an excellent manner … I recommend this book warmly as a rich source of information to everybody who is interested in 'Special Functions'.' Zentralblatt MATH' … this book contains a wealth of fascinating material which is presented in a user-friendly way. If you want to extend your knowledge of special functions, this is a good place to start. Even if your interests are in number theory or combinatorics, there is something for you too … the book can be warmly recommended and should be in all good libraries.' Adam McBride, The Mathematical Gazette' … it comes into the range of affordable books that you want to (and probably should have on your desk'. Jean Mawhin, Bulletin of the Belgian Mathematical Society'The book is full of beautiful and interesting formulae, as was always the case with mathematics centred around special functions. It is written in the spirit of the old masters, with mathemtics developed in terms of formulas. There are many historical comments in the book. It can be recommended as a very useful reference.' European Mathematical Society'… full of beautiful and interesting formulae … It can be recommended as a very useful reference.' EMS Newsletter'a very erudite text and reference in special functions' Allen Stenger, MAA ReviewsTable of Contents1. The Gamma and Beta functions; 2. The hypergeometric functions; 3. Hypergeometric transformations and identities; 4. Bessel functions and confluent hypergeometric functions; 5. Orthogonal polynomials; 6. Special orthogonal transformations; 7. Topics in orthogonal polynomials; 8. The Selberg integral and its applications; 9. Spherical harmonics; 10. Introduction to q-series; 11. Partitions; 12. Bailey chains; Appendix 1. Infinite products; Appendix 2. Summability and fractional integration; Appendix 3. Asymptotic expansions; Appendix 4. Euler-Maclaurin summation formula; Appendix 5. Lagrange inversion formula; Appendix 6. Series solutions of differential equations.
£56.99
Cambridge University Press A Brief Guide to Algebraic Number Theory 50 London Mathematical Society Student Texts Series Number 50
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£100.70
Cambridge University Press A Panorama of Number Theory or the View from Bakers Garden
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£122.55
Cambridge University Press Abelian Varieties Theta Functions and the Fourier Transform
Book SynopsisThe aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier–Mukai transform.Trade Review'The book is written by a leading expert in the field and it will certainly be a valuable enhancement to the existing literature.' EMS NewsletterTable of ContentsPart I. Analytic Theory: 1. Line bundles on complex tori; 2. Representations of Heisenberg groups I ; 3. Theta functions; 4. Representations of Heisenberg groups II: intertwining operators; 5. Theta functions II: functional equation; 6. Mirror symmetry for tori; 7. Cohomology of a line bundle on a complex torus: mirror symmetry approach; Part II. Algebraic Theory: 8. Abelian varieties and theorem of the cube; 9. Dual Abelian variety; 10. Extensions, biextensions and duality; 11. Fourier–Mukai transform; 12. Mumford group and Riemann's quartic theta relation; 13. More on line bundles; 14. Vector bundles on elliptic curves; 15. Equivalences between derived categories of coherent sheaves on Abelian varieties; Part III. Jacobians: 16. Construction of the Jacobian; 17. Determinant bundles and the principle polarization of the Jacobian; 18. Fay's trisecant identity; 19. More on symmetric powers of a curve; 20. Varieties of special divisors; 21. Torelli theorem; 22. Deligne's symbol, determinant bundles and strange duality; Bibliographical notes and further reading; References.
£105.45
Cambridge University Press Algorithmic Number Theory
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£152.95
Cambridge University Press Solving Polynomial Equation Systems I The KroneckerDuval Philosophy 88 Encyclopedia of Mathematics and its Applications Series Number 88
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£158.65
Cambridge University Press A Primer of Analytic Number Theory
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£114.00
Cambridge University Press The Prime Number Theorem 53 London Mathematical Society Student Texts Series Number 53
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£85.49
Cambridge University Press QuasiFrobenius Rings 158 Cambridge Tracts in Mathematics Series Number 158
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£105.45
Cambridge University Press Approximation by Algebraic Numbers
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£105.45
Cambridge University Press Automatic Sequences
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£81.69
Cambridge University Press Elementary Number Theory Group Theory and Ramanujan Graphs 55 London Mathematical Society Student Texts Series Number 55
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£138.70
Cambridge University Press Introductory Algebraic Number Theory
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£123.50
Cambridge University Press Hilberts Tenth Problem Diophantine Classes and Extensions to Global Fields 7 New Mathematical Monographs Series Number 7
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£105.45
Cambridge University Press Integer Partitions
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£138.70
Cambridge University Press Elementary Number Theory in Nine Chapters
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£94.99
Cambridge University Press Orthogonal Polynomials and Continued Fractions From Eulers Point of View Encyclopedia of Mathematics and its Applications Series Number 122
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£133.95
Cambridge University Press The Classical Fields Structural Features of the Real and Rational Numbers 112 Encyclopedia of Mathematics and its Applications Series Number 112
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£110.20
Cambridge University Press Galois Groups and Fundamental Groups 117
Book SynopsisEver since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level and assuming as little technical background as possible.Trade Review"The book is well written and contains much information about the etale fundamental group. There are exercises in every chapter. On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the etale fundamental group and the related Nori fundamental group scheme." Swaminathan Subramanian, Mathematical ReviewsTable of ContentsForeword; 1. Galois theory of fields; 2. Fundamental groups in topology; 3. Riemann surfaces; 4. Fundamental groups of algebraic curves; 5. Fundamental groups of schemes; 6. Tannakian fundamental groups; Bibliography; Index.
£57.94
Cambridge University Press LMSST 53 The Prime Number Theorem London Mathematical Society Student Texts Series Number 53
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£34.19
Cambridge University Press A HigherDimensional Sieve Method With Procedures for Computing Sieve Functions 177 Cambridge Tracts in Mathematics Series Number 177
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£105.45
Cambridge University Press Families of Varieties of General Type
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£123.50
Cambridge University Press Equivalents of the Riemann Hypothesis Volume 3 Further Steps towards Resolving the Riemann Hypothesis
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£142.50
Cambridge University Press Moonshine beyond the Monster
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£35.14
Cambridge University Press Modular Forms and String Theory
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£56.99
Cambridge University Press Elliptic Curves
Book Synopsis
£37.99
Cambridge University Press Multiplicative Number Theory I Classical Theory 97 Cambridge Studies in Advanced Mathematics Series Number 97
Book SynopsisPrime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In this 2006 text, the authors bring their extensive and distinguished research expertise to prepare the student for intelligent reading of the more advanced research literature.Trade Review'The text is very well written and accessible to students. On many occasions the authors explicitly describe basic methods known to everyone working in the field, but too often skipped in textbooks. This book may well become the standard introduction to analytic number theory.' Zentralblatt MATHTable of ContentsPreface; Notation; 1. Dirichlet series-I; 2. The elementary theory of arithmetic functions; 3. Principles and first examples of sieve methods; 4. Primes in arithmetic progressions-I; 5. Dirichlet series-II; 6. The prime number theorem; 7. Applications of the prime number theorem; 8. Further discussion of the prime number theorem; 9. Primitive characters and Gauss sums; 10. Analytic properties of the zeta function and L-functions; 11. Primes in arithmetic progressions-II; 12. Explicit formulae; 13. Conditional estimates; 14. Zeros; 15. Oscillations of error terms; Appendix A. The Riemann-Stieltjes integral; Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula; Appendix C. The gamma function; Appendix D. Topics in harmonic analysis.
£71.24
Cambridge University Press Vorlesungen uber Zahlentheorie Cambridge Library Collection Mathematics
Book SynopsisPeter Gustav Lejeune Dirichlet (1805â59) may be considered the father of modern number theory. He studied in Paris, coming under the influence of mathematicians like Fourier and Legendre, and then taught at Berlin and GÃttingen universities, where he was the successor to Gauss. This book contains lectures on number theory given by Dirichlet in 1856â7. They include his famous proofs of the class number theorem for binary quadratic forms and the existence of an infinity of primes in every appropriate arithmetical progression. The material was first published in 1863 by Richard Dedekind (1831â1916), professor at Braunschweig, who had been a junior colleague of Dirichlet at GÃttingen. The second edition appeared in 1871; this reissue is of the third, revised and expanded, edition of 1879; a fourth edition appeared as late as 1894. The appendices contain further work by both Dirichlet and Dedekind.Table of ContentsVorwort; 1. Von der Theilbarkeit der Zahlen; 2. Von der Congruens der Zahlen; 3. Von den quadratischen Resten; 4. Von den quadratischen Formen; 5. Bestimmung der Anzahl der Classen; Supplemente.
£47.49