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

G.H. Hardy and Marcel Riesz: The General Theory Of Dirichlet's Series

Published $1915$, Cambridge University Press.

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Contents

I. INTRODUCTION

$I.1.(1)$

$I.1.(2)$

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 SERIES

BIBLIOGRAPHY