Book:G.H. Hardy/The General Theory of Dirichlet's Series

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G.H. Hardy and Marcel Riesz: Introduction to Analytic Number Theory

Published $\text {1915}$, Cambridge University Press

Subject Matter

Dirichlet Series


Preface (G.H.H. 19 May 1915.)

$\text{I}$. Introduction
$\text{II}$. Elementary theory of the convergence of dirichlet's series
$\text{III}$. The formula for the sum of the coefficients of a dirichlet's series: the order of the function represented by the series
$\text{IV}$. The summation of the series by typical means
$\text{V}$. General arithmetic theorems concerning typical means
$\text{VI}$. Abelian and tauberian theorems
$\text{VII}$. Further developments in the series of functions represented by dirichlet's series
$\text{VIII}$. The multiplication of dirichlet's series