A primer of analytic number theory

From Pythagoras to Riemann

Jeffrey Stopple

396 pages, parution le 22/10/2003

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Résumé

This undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.

Sums and differences
Products and divisibility
Order and magnitude
Averages
Calculus
Prime
Series
Basel problem
Euler's product
Complex numbers
The Riemann zeta function
Symmetry
Explicit formula
Modular arithmetic
Pell's equation
Elliptic curves
Analytic theory of algebraic numbers
Solutions
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Jeffrey Stopple
Parution	22/10/2003
Nb. de pages	396
Format	15 x 22,7
Couverture	Broché
Poids	535g
Intérieur	Noir et Blanc
EAN13	9780521012539
ISBN13	978-0-521-01253-9