Number theory Books
Cambridge University Press Zeta Functions of Graphs A Stroll through the Garden 128 Cambridge Studies in Advanced Mathematics Series Number 128
Book SynopsisThis stimulating introduction to zeta (and related) functions of graphs develops the fruitful analogy between combinatorics and number theory - for example, the Riemann hypothesis for graphs - making connections with quantum chaos, random matrix theory, and computer science. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.Trade Review'The book is very appealing through its informal style and the variety of topics covered and may be considered the standard reference book in this field.' Zentralblatt MATHTable of ContentsList of illustrations; Preface; Part I. A Quick Look at Various Zeta Functions: 1. Riemann's zeta function and other zetas from number theory; 2. Ihara's zeta function; 3. Selberg's zeta function; 4. Ruelle's zeta function; 5. Chaos; Part II. Ihara's Zeta Function and the Graph Theory Prime Number Theorem: 6. Ihara zeta function of a weighted graph; 7. Regular graphs, location of poles of zeta, functional equations; 8. Irregular graphs: what is the RH?; 9. Discussion of regular Ramanujan graphs; 10. The graph theory prime number theorem; Part III. Edge and Path Zeta Functions: 11. The edge zeta function; 12. Path zeta functions; Part IV. Finite Unramified Galois Coverings of Connected Graphs: 13. Finite unramified coverings and Galois groups; 14. Fundamental theorem of Galois theory; 15. Behavior of primes in coverings; 16. Frobenius automorphisms; 17. How to construct intermediate coverings using the Frobenius automorphism; 18. Artin L-functions; 19. Edge Artin L-functions; 20. Path Artin L-functions; 21. Non-isomorphic regular graphs without loops or multiedges having the same Ihara zeta function; 22. The Chebotarev Density Theorem; 23. Siegel poles; Part V. Last Look at the Garden: 24. An application to error-correcting codes; 25. Explicit formulas; 26. Again chaos; 27. Final research problems; References; Index.
£59.84
Cambridge University Press Lectures on Algebraic Cycles
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£59.84
Cambridge University Press A Mathematical Tapestry Demonstrating the Beautiful Unity of Mathematics
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£26.59
Cambridge University Press Introduction to Modern Prime Number Theory
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£39.89
Cambridge University Press Period Domains over Finite and padic Fields 183 Cambridge Tracts in Mathematics Series Number 183
Book SynopsisThis book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.Trade Review'This monograph is a systematic treatise on period domains over finite and over p-adic fields. It presents the theory as it has developed over the past fifteen years … The book should serve as the basis of future research in this area.' Zentralblatt MATHTable of ContentsPreface; Introduction; Part I. Period Domains for GLn Over a Finite Field: 1. Filtered vector spaces; 2. Period domains for GLn; 3. Cohomology of period domains for GLn; Part II. Period Domains for Reductive Groups over Finite Fields: 4. Interlude on the Tannakian formalism; 5. Filtrations on repk(G); 6. Period domains for reductive groups; 7. Cohomology of period domains for reductive groups; Part III. Period Domains over p-adic Fields: 8. Period domains over p-adic fields; 9. Period domains for p-adic reductive groups; 10. Cohomology of period domains over p-adic fields; Part IV. Complements: 11. Further aspects of period domains; References; Index.
£122.55
Cambridge University Press Algorithmic Number Theory Lattices Number Fields Curves and Cryptography 44 Mathematical Sciences Research Institute Publications Series Number 44
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£49.39
Cambridge University Press Diophantine Equations over Function Fields 96 London Mathematical Society Lecture Note Series Series Number 96
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£45.16
Cambridge University Press Concise Intro Theory of Numbers
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£41.79
Cambridge University Press Diophantine Analysis Proceedings At The Number Theory Section Of The 1985 Australian Mathematical Society Convention 109 London Mathematical Society Lecture Note Series Series Number 109
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£47.63
Cambridge University Press LMS 126 Van der Corputs Method London Mathematical Society Lecture Note Series Series Number 126
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£51.99
Cambridge University Press LMS 134 Number Theory Dynamical London Mathematical Society Lecture Note Series Series Number 134
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£55.09
Cambridge University Press LMS 153 L Functions and Arithmetic London Mathematical Society Lecture Note Series Series Number 153
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£74.13
Cambridge University Press Number Theory and Cryptography 154 London Mathematical Society Lecture Note Series Series Number 154
Book SynopsisIn this volume, originally published in 1990, are included papers presented at two meetings; one a workshop on Number Theory and Cryptography, and the other, the annual meeting of the Australian Mathematical Society. Questions in number theory are of military and commercial importance for the security of communication, as they are related to codes and code-breaking. Papers in the volume range from problems in pure mathematics whose study has been intensified by this connection, through interesting theoretical and combinatorial problems which arise in the implementation, to practical questions that come from banking and telecommunications. The contributors are prominent within their field. The whole volume will be an attractive purchase for all number theorists, 'pure' or 'applied'.Table of ContentsList of contributors; Introduction; Part I. Number Theoretic Aspects of Cryptology: 1. Some mathematical aspects of recent advances in cryptology R. Lidl; 2. Quadratic fields and cryptography J. Buchmann and H. C. Williams; 3. Parallel algorithms for integer factorisation R. P. Brent; 4. An open architecture number sieve A. J. Stephens and H. C. Williams; 5. Algorithms for finite fields H. W. Lenstra, Jr.; 6. Notes on continued fractions and recurrence sequences A. J. Van der Poorten; Part II. Cryptographic Devices and Applications: 7. Security in telecommunication services over the next decade J. Snare; 8. Linear feedback shift registers and stream ciphers E. Dawson; 9. Applying randomness tests to commercial level block ciphers H. Gustaphson, E. Dawson and W. Caelli; 10. Pseudo-random sequence generators using structures noise R. S. Safavi-Naini and J. R. Seberry; 11. Privacy for MANCET M. Warner; 12. Authentication B. Newman; 13. Insecurity of the knapsack one-time pad R. T. Worley; 14. The tactical frequency management problem: heuristic search and simulated annealing L. Peters; 15. Reed–Solomon coding in the complex field M. Rudolph; Part III. Diophantine Analysis: 16. Class number problems for real quadratic fields R. A. Mollin and H. C. Williams; 17. Number theoretic problems involving two independent bases T. Kamae; 18. A class of normal numbers II. Y. -N. Nakai and I. Shiokawa; 19. Notes on uniform distribution G. Myerson and A. Pollington; 20. Thue equations and multiplicative independence B. Brizinda; 21. A number theoretic crank associated with open bosonic strings F. G. Garvan; 22. Universal families of abelian varieties A. Silverberg.
£45.16
Cambridge University Press Spectral Decomposition and Eisenstein Series A Paraphrase of the Scriptures 113 Cambridge Tracts in Mathematics Series Number 113
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£122.55
Cambridge University Press London Mathematical Society Student Texts 24 Lectures on Elliptic Curves 0024 London Mathematical Society Student Texts Series Number 24
Book SynopsisThe study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no Trade Review'… an excellent introduction … written with humour.' Monatshefte für MathematikTable of ContentsIntroduction; 1. Curves of genus: introduction; 2. p-adic numbers; 3. The local-global principle for conics; 4. Geometry of numbers; 5. Local-global principle: conclusion of proof; 6. Cubic curves; 7. Non-singular cubics: the group law; 8. Elliptic curves: canonical form; 9. Degenerate laws; 10. Reduction; 11. The p-adic case; 12. Global torsion; 13. Finite basis theorem: strategy and comments; 14. A 2-isogeny; 15. The weak finite basis theorem; 16. Remedial mathematics: resultants; 17. Heights: finite basis theorem; 18. Local-global for genus principle; 19. Elements of Galois cohomology; 20. Construction of the jacobian; 21. Some abstract nonsense; 22. Principle homogeneous spaces and Galois cohomology; 23. The Tate-Shafarevich group; 24. The endomorphism ring; 25. Points over finite fields; 26. Factorizing using elliptic curves; Formulary; Further reading; Index.
£35.14
Cambridge University Press Arithmetical Functions 184 London Mathematical Society Lecture Note Series Series Number 184
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£50.99
Cambridge University Press Elementary Theory of Lfunctions and Eisenstein Series 26 London Mathematical Society Student Texts Series Number 26
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£133.95
Cambridge University Press Elementary Theory of Lfunctions and Eisenstein Series 26 London Mathematical Society Student Texts Series Number 26
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£71.24
Cambridge University Press Algebraic Curves over Finite Fields Errorcorrecting Codes and Exponential Sums Cambridge Tracts in Mathematics Series Number 97
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£53.19
Cambridge University Press LMS 217 Quadratic Forms Appllctns London Mathematical Society Lecture Note Series Series Number 217
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£50.95
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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£122.55
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.
£102.60
Cambridge University Press LMS 230 Prolegomena to Middlebrow London Mathematical Society Lecture Note Series Series Number 230
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£67.51
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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£45.16
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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£46.54
Cambridge University Press Analytic Number Theory Essays in Honour of Klaus Roth
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£128.25
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.
£54.14
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.
£37.99
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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£65.86
Cambridge University Press LMS 215 Number Theory Paris 19923 London Mathematical Society Lecture Note Series Series Number 215
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£65.86
Cambridge University Press Duality in Analytic Number Theory 122 Cambridge Tracts in Mathematics Series Number 122
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£122.55
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.
£45.59
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.
£128.25
Cambridge University Press A Pathway into Number Theory 2ed
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£48.44
Cambridge University Press Automorphic Forms on SL2 R 130 Cambridge Tracts in Mathematics Series Number 130
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£105.45
Cambridge University Press LMS 237 Sieve Methods London Mathematical Society Lecture Note Series Series Number 237
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£65.86
Cambridge University Press Algorithmic Algebraic Number Theory 30 Encyclopedia of Mathematics and its Applications Series Number 30
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£79.10
Cambridge University Press Elementary Number Theory in Nine Chapters
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£42.74
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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£78.28
Cambridge University Press Special Functions 71 Encyclopedia of Mathematics and its Applications Series Number 71
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£139.65
Cambridge University Press LMS 247 Analytic Number Theory London Mathematical Society Lecture Note Series Series Number 247
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£61.71
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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£48.44
Cambridge University Press Aspects of Galois Theory 256 London Mathematical Society Lecture Note Series Series Number 256
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£61.71
Cambridge University Press The Theory of Partitions 2 Encyclopedia of Mathematics and its Applications Series Number 2
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£52.24
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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£116.85
Cambridge University Press Character Sums with Exponential Functions and their Applications 136 Cambridge Tracts in Mathematics Series Number 136
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£105.45
Cambridge University Press Arithmetic of Quadratic Forms 106 Cambridge Tracts in Mathematics Series Number 106
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£53.43