Warenkorb
€ 0,00 0 Buch dabei,
portofrei
Sums of Squares of Integers als Buch
PORTO-
FREI

Sums of Squares of Integers

Sprache: Englisch.
Buch (gebunden)
Ihr 12%-Rabatt auf alle Spielwaren, Hörbücher, Filme, Musik u.v.m
 
12% Rabatt sichern mit Gutscheincode: NIKOLAUS12
 
Sums of Squares of Integers is the first book to combine elementary methods with analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representatio … weiterlesen
Buch

136,99 *

inkl. MwSt.
Portofrei
Lieferbar innerhalb von zwei Wochen
Sums of Squares of Integers als Buch

Produktdetails

Titel: Sums of Squares of Integers
Autor/en: Carlos J. Moreno, Samuel S. Jr. Wagstaff

ISBN: 1584884568
EAN: 9781584884569
Sprache: Englisch.
CHAPMAN & HALL

Dezember 2005 - gebunden - 354 Seiten

Beschreibung

Sums of Squares of Integers is the first book to combine elementary methods with analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares for any s and n. This book is also the first to give a proof of Szemeredi's theorem, an important result in modern number theory. It discusses how the modern theory of modular forms complements and clarifies the classical, fundamental results about sums of squares. This text includes applications to such diverse fields as cryptography, crystallography, and thermal radiation. Written by world-class experts, this book is ideal for mathematicians, particularly number theorists and computer scientists.

Inhaltsverzeichnis

Introduction Prerequisites Outline of Chapters 2 - 8 Elementary Methods Introduction Some Lemmas Two Fundamental Identities Euler's Recurrence for Sigma(n) More Identities Sums of Two Squares Sums of Four Squares Still More Identities Sums of Three Squares An Alternate Method Sums of Polygonal Numbers Exercises Bernoulli Numbers Overview Definition of the Bernoulli Numbers The Euler-MacLaurin Sum Formula The Riemann Zeta Function Signs of Bernoulli Numbers Alternate The von Staudt-Clausen Theorem Congruences of Voronoi and Kummer Irregular Primes Fractional Parts of Bernoulli Numbers Exercises Examples of Modular Forms Introduction An Example of Jacobi and Smith An Example of Ramanujan and Mordell An Example of Wilton: t (n) Modulo 23 An Example of Hamburger Exercises Hecke's Theory of Modular Forms Introduction Modular Group ? and its Subgroup ? 0 (N) Fundamental Domains For ? and ? 0 (N) Integral Modular Forms Modular Forms of Type Mk(? 0(N);chi) and Euler-Poincare series Hecke Operators Dirichlet Series and Their Functional Equation The Petersson Inner Product The Method of Poincare Series Fourier Coefficients of Poincare Series A Classical Bound for the Ramanujan t function The Eichler-Selberg Trace Formula l-adic Representations and the Ramanujan Conjecture Exercises Representation of Numbers as Sums of Squares Introduction The Circle Method and Poincare Series Explicit Formulas for the Singular Series The Singular Series Exact Formulas for the Number of Representations Examples: Quadratic Forms and Sums of Squares Liouville's Methods and Elliptic Modular Forms Exercises Arithmetic Progressions Introduction Van der Waerden's Theorem Roth's Theorem t 3 = 0 Szemeredi's Proof of Roth's Theorem Bipartite Graphs Configurations More Definitions The Choice of tm Well-Saturated K-tuples Szemeredi's Theorem Arithmetic Progressions of Squares Exercises Applications Factoring Integers Computing Sums of Two Squares Computing Sums of Three Squares Computing Sums of Four Squares Computing rs(n) Resonant Cavities Diamond Cutting Cryptanalysis of a Signature Scheme Exercises References Index

Pressestimmen

"provides an excellent supplementary source of information for the reader, not least in the many biographical footnotes on the mathematicians involved in the subject matter, and there are also more than a thousand exercises and examples in the text. Besides various tables for results in computational number theory, the nine appendices cover material from set theory, which includes discussions on the axiom of choice and Zorn's Lemma, to the ABC conjecture." --P. Shiu, Zentralblatt MATH, Vol. 943 ides an excellent supplementary source of information for the reader, not least in the many biographical footnotes on the mathematicians involved in the subject matter, and there are also more than a thousand exercises and examples in the text. Besides various tables for results in computational number theory, the nine appendices cover material from set theory, which includes discussions on the axiom of choice and Zorn's Lemma, to the ABC conjecture." --P. Shiu, Zentralblatt MATH, Vol. 943 "This is a remarkable book that will be a valuable reference for many people, including me. The book shows great care in preparation, and the ample details and motivation will be appreciated by lots of students. The solid punches at the end of each chapter will be appreciated by everybody. It deserves success with many adoptions as a text." --Irving Kaplansky, Mathematical Sciences Research Institute at Berkeley is a remarkable book that will be a valuable reference for many people, including me. The book shows great care in preparation, and the ample details and motivation will be appreciated by lots of students. The solid punches at the end of each chapter will be appreciated by everybody. It deserves successwith many adoptions as a text." --Irving Kaplansky, Mathematical Sciences Research Institute at Berkeley "This is a great book! It can be used in many ways: for a university course at one extreme, and as selective light reading for pleasure at the other. The author's enthusiasm carries the reader along clearly and easily, spilling over to scores of fascinating, beautifully written footnotes, which include more than fifty mini-biographies. excellent and highly recommended." --Short Book Reviews, Vol. 21, No. 2, August, 2001 is a great book! It can be used in many ways: for a university course at one extreme, and as selective light reading for pleasure at the other. The author's enthusiasm carries the reader along clearly and easily, spilling over to scores of fascinating, beautifully written footnotes, which include more than fifty mini-biographies. excellent and highly recommended." --Short Book Reviews, Vol. 21, No. 2, August, 2001

Mehr aus dieser Reihe

zurück
Combinatorial Algorithms: Generation, Enumberation, and Search
Buch (gebunden)
von Donald L. Kreher…
Applied Mathematical Modeling
Buch (gebunden)
Advanced Number Theory with Applications
Buch (gebunden)
von Richard A. Molli…
How to Count: An Introduction to Combinatorics, Second Edition
Buch (gebunden)
von Alan Slomson, R.…
Introduction to Information Theory and Data Compression, Second Edition
Buch (gebunden)
von Peter D. Johnson…
vor
Servicehotline
089 - 70 80 99 47

Mo. - Fr. 8.00 - 20.00 Uhr
Sa. 10.00 - 20.00 Uhr
Filialhotline
089 - 30 75 75 75

Mo. - Sa. 9.00 - 20.00 Uhr
Bleiben Sie in Kontakt:
Sicher & bequem bezahlen:
akzeptierte Zahlungsarten: Überweisung, offene Rechnung,
Visa, Master Card, American Express, Paypal
Zustellung durch:
* Alle Preise verstehen sich inkl. der gesetzlichen MwSt. Informationen über den Versand und anfallende Versandkosten finden Sie hier.
** Deutschsprachige eBooks und Bücher dürfen aufgrund der in Deutschland geltenden Buchpreisbindung und/oder Vorgaben von Verlagen nicht rabattiert werden. Soweit von uns deutschsprachige eBooks und Bücher günstiger angezeigt werden, wurde bei diesen kürzlich von den Verlagen der Preis gesenkt oder die Buchpreisbindung wurde für diese Titel inzwischen aufgehoben. Angaben zu Preisnachlässen beziehen sich auf den dargestellten Vergleichspreis.