Introduction to Analytic Number Theory

Inbunden, Engelska, 1976

AvTom M. Apostol

779 kr

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This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

Produktinformation

Utgivningsdatum1976-05-11
Mått155 x 235 x 27 mm
Vikt698 g
FormatInbunden
SpråkEngelska
SerieUndergraduate Texts in Mathematics
Antal sidor340
FörlagSpringer-Verlag New York Inc.
ISBN9780387901633

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Talteori inom Naturvetenskap och teknik

Historical Introduction.- 1 The Fundamental Theorem of Arithmetic.- 2 Arithmetical Functions and Dirichlet Multiplication.- 3 Averages of Arithmetical Functions.- 4 Some Elementary Theorems on the Distribution of Prime Numbers.- 5 Congruences.- 6 Finite Abelian Groups and Their Characters.- 7 Dirichlet’s Theorem on Primes in Arithmetic Progressions.- 8 Periodic Arithmetical Functions and Gauss Sums.- 9 Quadratic Residues and the Quadratic Reciprocity Law.- 10 Primitive Roots.- 11 Dirichlet Series and Euler Products.- 12 The Functions ?(s) and L(s, ?).- 13 Analytic Proof of the Prime Number Theorem.- 14 Partitions.- Index of Special Symbols.

From the reviews: T.M. Apostol Introduction to Analytic Number Theory "This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read." -MATHEMATICAL REVIEWS "After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. ... I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains its own set of ... exercises. ... this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory." (Alvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)