General Theory of Dirichlet's Series

Includes bibliography (p. 69-78) and references

I
INTRODUCTION
II
ELEMENTARY THEORY OF THE CONVERGENCE OF DIRICHLET�S SERIES
III
THE FORMULA FOR THE SUM OF THE COEFFICIENTS OF A DIRICHLET�S SERIES: THE ORDER OF THE FUNCTION REPRESENTED BY THE SERIES
IV
THE SUMMATION OF SERIES BY TYPICAL MEANS
V
GENERAL ARITHMETIC THEOREMS CONCERNING TYPICAL MEANS
VI
ABELIAN AND TAUBERIAN THEOREMS
VII
FURTHER DEVELOPMENTS OF THE THEORY OF FUNCTIONS REPRESENTED BY DIRICHLET�S SERIES VIII
THE MULTIPLICATION OF DIRICHLET�S SERIESBIBLIOGRAPHY
DOVER PHOENIX EDITIONS

This 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 conver.