An Introduction to the Analytic Theory of NumbersThe mathematical preparation is relatively modest: the elements of number theory, algebra, and group theory are required. A good working knowledge of element of complex function theory and general analytic processes is needed. The subject matter is of varying difficulty, and while the first chapter reads relatively easily, subsequent chapters require close attention. The subject of analytic number theory is not clearly defined. While the choice of topics included herein is somewhat arbitrary, the topics themselves represent some important problems of number theory to which generations of outstanding mathematicians have contributed. |
Contents
Dirichlets theorem on primes in an arithmetic progression | 1 |
The theory of partitions | 135 |
Warings problem | 206 |
Copyright | |
2 other sections not shown
Other editions - View all
Common terms and phrases
addition analytic apply argument arithmetic assume bounded calculate called Chapter character choose circle complete Consequently consider constant converges corollary deduce defined definition denote depends derive determined Dirichlet series discriminant equation equivalent estimate evaluate example exists fact factor Farey field fixed follows formula function fundamental give given hand hence holds hypothesis ideals implies important inequality infer infinitely integral interesting interval Lemma means method MICHIGAN modulo Moreover multiplicative natural number theorem particular partitions points positive possible precise prime prime number problem proof properties prove quadratic ranges regular relation remains replace residue result satisfies shown side solutions square summation Suppose term theory transformation Σ Σ