## The General Theory of Dirichlet's SeriesThis classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians of the twentieth century: G. H. Hardy is famous for his achievements in number theory and mathematical analysis, and Marcel Riesz's interests ranged from functional analysis to partial differential equations, mathematical physics, number theory, and algebra. Following an introduction, the authors proceed to a discussion of the elementary theory of the convergence of Dirichlet's series, followed by a look at the formula for the sum of the coefficients of a Dirichlet's series in terms of the order of the function represented by the series. They continue with an examination of the summation of series by typical means and of general arithmetic theorems concerning typical means. After a survey of Abelian and Tauberian theorems and of further developments of the theory of functions represented by Dirichlet's series, the text concludes with an exploration of the multiplication of Dirichlet's series. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

abscissa absolutely convergent apply argument Bohr Cesaro's Chapman choose coefficient complete Comptes Rendus concerning condition consider constant contains deduce defined definitions depends Dirichlet's series edition equation established evident example existence expression extended figures finite order follows formula function Further generalisation give given greater half-plane Hardy Hence holds important increase inequalities infinity integral interesting Journal kind Landau Lemma less limit Littlewood Lond Math mean value theorem methods multiple necessary observe obtain ordinary Dirichlet's series original particular positive possible power series Proc proof proved reader region regular Reihen relation remains replaced represents result Riesz satisfied séries series is convergent series is summable shown simple substitute sufficiently summation suppose tends term Theorem theory throughout true typical means Unabridged republication values write zero