Number theory Books
Cambridge University Press Arithmetical Functions 184 London Mathematical Society Lecture Note Series Series Number 184
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£60.75
Cambridge University Press Elementary Theory of Lfunctions and Eisenstein Series 26 London Mathematical Society Student Texts Series Number 26
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£141.00
Cambridge University Press Elementary Theory of Lfunctions and Eisenstein Series 26 London Mathematical Society Student Texts Series Number 26
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£74.99
Cambridge University Press Spectral Theory of the Riemann ZetaFunction 127 Cambridge Tracts in Mathematics Series Number 127
Book SynopsisThe Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the develoTrade ReviewReview of the hardback: '… gives an excellent presentation of the interplay between the Riemann zeta function and automorphic forms … nicely written and of great interest for any number theorists.' R. Tichy, International Mathematical NewsTable of Contents1. Non-Euclidean harmonics; 2. Trace formulas; 3. Automorphic L-functions; 4. An explicit formula; 5. Asymptotics; References; Index.
£111.00
Cambridge University Press Algebraic Curves over Finite Fields Errorcorrecting Codes and Exponential Sums Cambridge Tracts in Mathematics Series Number 97
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£55.99
Cambridge University Press LMS 217 Quadratic Forms Appllctns London Mathematical Society Lecture Note Series Series Number 217
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£49.13
Cambridge University Press Cohomology of Drinfeld Modular Varieties Part 1 Geometry Counting of Points and Local Harmonic Analysis Cambridge Studies in Advanced Mathematics Series Number 41
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£129.00
Cambridge University Press Automorphic Representations and LFunctions for the General Linear Group Volume 1 129 Cambridge Studies in Advanced Mathematics Series Number 129
Book SynopsisThis graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.Trade Review'In this book, the authors give a thorough yet elementary introduction to the theory of automorphic forms and L-functions for the general linear group of rank two over rational adeles … The exposition is accompanied by exercises after every chapter. Definitions are repeated when needed, and previous results are always cited, so the book is very accessible.' Marcela Hanzer, Zentralblatt MATHTable of ContentsPreface; 1. Adeles over Q; 2. Automorphic representations and L-functions for GL(1,AQ); 3. The classical theory of automorphic forms for GL(2); 4. Automorphic forms for GL(2,AQ); 5. Automorphic representations for GL(2,AQ); 6. Theory of admissible representations of GL(2,Qp); 7. Theory of admissible (g,K∞) modules for GL(2,R); 8. The contragredient representation for GL(2); 9. Unitary representations of GL(2); 10. Tensor products of local representations; 11. The Godement–Jacquet L-function for GL(2,AQ); Solutions to selected exercises; References; Symbols index; Index.
£108.00
Cambridge University Press LMS 230 Prolegomena to Middlebrow London Mathematical Society Lecture Note Series Series Number 230
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£70.93
Cambridge University Press Modular Forms on Schiermonnikoog
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£122.55
Cambridge University Press Arithmetic of Diagonal Hypersurfaces over Finite Fields
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£45.49
Cambridge University Press An Introduction to the Theory of the Riemann ZetaFunction 14 Cambridge Studies in Advanced Mathematics Series Number 14
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£57.13
Cambridge University Press Analytic Number Theory Essays in Honour of Klaus Roth
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£135.00
Cambridge University Press A Computational Introduction to Number Theory and Algebra World Trade Organization
Book SynopsisThis introductory book emphasizes algorithms and applications, and is accessible to a broad audience. The author alternates between theory and applications in order to illustrate the mathematics. This second edition includes many new exercises and worked examples, and has been reorganized to improve presentation and clarity of exposition.Trade Review'The subject matter is presented in a very thorough way … The material is very well organized: definitions, results and their interrelations fit together perfectly … The book is especially attractive to students with a background or interest in computer science … The suitability of the book for self-study is greatly enhanced by a wealth of exercises and examples that are provided … the book is very well-written, and it is a pleasure to read.' Mathematics of Computation'… the book could serve as a course of discrete mathematics for computer science students.' EMS NewsletterTable of ContentsPreface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid's algorithm; 5. The distribution of primes; 6. Abelian groups; 7. Rings; 8. Finite and discrete probability distributions; 9. Probabilistic algorithms; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Z*p; 12. Quadratic reciprocity and computing modular square roots; 13. Modules and vector spaces; 14. Matrices; 15. Subexponential-time discrete logarithms and factoring; 16. More rings; 17. Polynomial arithmetic and applications; 18. Linearly generated sequences and applications; 19. Finite fields; 20. Algorithms for finite fields; 21. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.
£56.99
Cambridge University Press Elementary Number Theory Group Theory and Ramanujan Graphs
Book SynopsisThis text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.Trade Review'The book under review is an attractively written excellent text which successfully bridges the gap between undergraduate instruction and current research. Hence it is very well suited to bring a fresh breeze into the classroom. The reviewer warmly recommends this text to any lecturer looking for an attractive theme and to everybody else for great supplementary reading. Of course, this book should not be missed in any institutional library.' Zentralblatt MATH'A light touch and the inclusion of some unexpected results make the book a pleasure to read.' MathematikaTable of ContentsAn overview; 1. Graph theory; 2. Number theory; 3. PSL2(q); 4. The graphs Xp,q; Appendix A. 4-regular graphs with large girth; Index; Bibliography.
£47.26
Cambridge University Press Transcendental Aspects of Algebraic Cycles Proceedings of the Grenoble Summer School 2001 313 London Mathematical Society Lecture Note Series Series Number 313
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£69.48
Cambridge University Press LMS 215 Number Theory Paris 19923 London Mathematical Society Lecture Note Series Series Number 215
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£69.48
Cambridge University Press Duality in Analytic Number Theory 122 Cambridge Tracts in Mathematics Series Number 122
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£129.00
Cambridge University Press Theory of Algebraic Integers
Book SynopsisDedekind memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in installments in French in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome.Trade Review"The book has historical interest in providing a very clear glimpse of the origins of modern algebra and algebraic number theory, but it also has considerable mathematical interest. It is truly astonishing that a text written one hundred and twenty years ago, well before modern algebraic terminology and concepts were introduced and accepted, can provide a plausible introduction to algebraic number theory for a student today." Mathematical Reviews Clippings 98hTable of ContentsPart I. Translator's Introduction: 1. General remarks; 2. Squares; 3. Quadratic forms; 4. Quadratic integers; 5. Roots of unity; 6. Algebraic integers; 7. The reception of ideal theory; Part II. Theory of Algebraic Integers: 8. Auxiliary theorems from the theory of modules; 9. Germ of the theory of ideals; 10. General properties of algebraic integers; 11. Elements of the theory of ideals.
£56.16
Cambridge University Press The HardyLittlewood Method 125 Cambridge Tracts in Mathematics Series Number 125
Book SynopsisThis introduction to the Hardy-Littlewood method deals with its classical forms and outlines some of the more recent developments. Now in its second edition, it has been fully updated, and covers recent developments in detail. It is the standard reference on the Hardy-Littlewood method.Trade Review'Now in its second edition, it has been fully updated; extensive revisions have been made and a new chapter added to take account of major advances.' L'Enseignement MathématiqueTable of Contents1. Introduction and historical background; 2. The simplest upper bound for G(k); 3. Goldbach's problems; 4. The major arcs in Waring's problem; 5. Vinogradov's methods; 6. Davenport's methods; 7. Vinogradov's upper bound for G(k); 8. A ternary additive problem; 9. Homogenous equations and Birch's theorem; 10. A theorem of Roth; 11. Diophantine inequalities; 12. Wooley's upper bound for G(k); Bibliography.
£135.00
Cambridge University Press A Pathway into Number Theory 2ed
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£59.11
Cambridge University Press Automorphic Forms on SL2 R 130 Cambridge Tracts in Mathematics Series Number 130
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£111.00
Cambridge University Press LMS 235 Number Theory Sminaire de thorie des nombres de Paris 199394 Sminaire de thorie des nombres de Paris 199394 London Mathematical Society Lecture Note Series Series Number 235
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£45.49
Cambridge University Press LMS 237 Sieve Methods London Mathematical Society Lecture Note Series Series Number 237
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£69.48
Cambridge University Press Algorithmic Algebraic Number Theory 30 Encyclopedia of Mathematics and its Applications Series Number 30
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£93.72
Cambridge University Press Analytic Methods for Diophantine Equations and Diophantine Inequalities
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£56.16
Cambridge University Press Elementary Number Theory in Nine Chapters
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£52.20
Cambridge University Press Recent Perspectives in Random Matrix Theory and Number Theory 322 London Mathematical Society Lecture Note Series Series Number 322
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£84.02
Cambridge University Press Special Functions 71 Encyclopedia of Mathematics and its Applications Series Number 71
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£147.00
Cambridge University Press LMS 247 Analytic Number Theory London Mathematical Society Lecture Note Series Series Number 247
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£64.39
Cambridge University Press Representations and Cohomology v1 Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras Cambridge Studies in Advanced Mathematics Series Number 30
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£59.11
Cambridge University Press Aspects of Galois Theory 256 London Mathematical Society Lecture Note Series Series Number 256
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£64.39
Cambridge University Press The Theory of Partitions 2 Encyclopedia of Mathematics and its Applications Series Number 2
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£54.99
Cambridge University Press The Algorithmic Resolution of Diophantine Equations A Computational Cookbook 41 London Mathematical Society Student Texts Series Number 41
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£123.00
Cambridge University Press Character Sums with Exponential Functions and their Applications 136 Cambridge Tracts in Mathematics Series Number 136
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£111.00
Cambridge University Press LMS 254 Galois Repres Algebra Geom London
Book SynopsisThis book has its origins in the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. Included here are expositions of subjects on the interface between algebraic number theory and arithmetic algebraic geometry which have received substantial attention from many of the best known researchers in this field.Table of ContentsPreface; List of participants; Lecture programme; 1. The Eigencurve R. Coleman and B. Mazur; 2. Geometric trends in Galois module theory Boas Erez; 3. Mixed elliptic motives Alexander Goncharov; 4. On the Satake isomorphism Benedict H. Gross; 5. Open problems regarding rational points on curves and varieties B. Mazur; 6. Models of Shimura varieties in mixed characteristics Ben Moonen; 7. Euler systems and modular elliptic curves Karl Rubin; 8. Basic notions of rigid analytic geometry Peter Schneider; 9. An introduction to Kato's Euler systems A. J. Scholl; 10. La distribution d'Euler-Poincaré d'un groupe profini Jean-Pierre Serre.
£73.12
Cambridge University Press Arithmetic of Quadratic Forms 106 Cambridge Tracts in Mathematics Series Number 106
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£63.07
Cambridge University Press Elliptic Curves in Cryptography 265 London Mathematical Society Lecture Note Series Series Number 265
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£65.99
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.
£59.99
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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£78.93
Cambridge University Press LFunctions and Galois Representations 320 London Mathematical Society Lecture Note Series Series Number 320
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£95.66
Cambridge University Press Heights in Diophantine Geometry 4 New Mathematical Monographs Series Number 4
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£65.99
Cambridge University Press Number Theory and Polynomials London Mathematical Society Lecture Note Series Series Number 352
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£64.39
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.
£39.99
Cambridge University Press Elliptic Curves and Big Galois Representations London Mathematical Society Lecture Note Series Series Number 356
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£78.93
Cambridge University Press A Mathematical Tapestry
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£79.99
Cambridge University Press Complex Multiplication 15 New Mathematical Monographs Series Number 15
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£129.00
Cambridge University Press Modular Forms and Galois Cohomology 69 Cambridge Studies in Advanced Mathematics Series Number 69
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£129.00
