The General Theory of Dirichlet's Series
From the PREFACE.
THE publication of this tract has been delayed by a variety of causes, and I am now compelled to issue it without Dr Riesz's help in the final correction of the proofs. This has at any rate, one advantage, that it gives me the opportunity of saying how conscious I am that whatever value it possesses is due mainly to his contributions to it, and in particular to the fact, that it contains the first systematic, account of his beautiful theory of the summation of series by 'typical means'.
The task of condensing any account of so extensive a theory into the compass of one of these tracts has proved an exceedingly difficult one. Many important theorems are stated without proof, and many details are left to the reader. I believe, however, that our account is full enough to serve as a guide to other mathematicians researching in this and allied subjects. Such readers will be familiar with Landau's Handbuch der Lehre con der Verteilung der Primzahlen, and will hardly need to be told how much we, in common with all other investigators in this field, owe to the writings and to the personal encouragement of its author.
G. H. H.
* * * * *
CONTENTS
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 Series
Bibliography
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THE publication of this tract has been delayed by a variety of causes, and I am now compelled to issue it without Dr Riesz's help in the final correction of the proofs. This has at any rate, one advantage, that it gives me the opportunity of saying how conscious I am that whatever value it possesses is due mainly to his contributions to it, and in particular to the fact, that it contains the first systematic, account of his beautiful theory of the summation of series by 'typical means'.
The task of condensing any account of so extensive a theory into the compass of one of these tracts has proved an exceedingly difficult one. Many important theorems are stated without proof, and many details are left to the reader. I believe, however, that our account is full enough to serve as a guide to other mathematicians researching in this and allied subjects. Such readers will be familiar with Landau's Handbuch der Lehre con der Verteilung der Primzahlen, and will hardly need to be told how much we, in common with all other investigators in this field, owe to the writings and to the personal encouragement of its author.
G. H. H.
* * * * *
CONTENTS
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 Series
Bibliography
The General Theory of Dirichlet's Series
From the PREFACE.
THE publication of this tract has been delayed by a variety of causes, and I am now compelled to issue it without Dr Riesz's help in the final correction of the proofs. This has at any rate, one advantage, that it gives me the opportunity of saying how conscious I am that whatever value it possesses is due mainly to his contributions to it, and in particular to the fact, that it contains the first systematic, account of his beautiful theory of the summation of series by 'typical means'.
The task of condensing any account of so extensive a theory into the compass of one of these tracts has proved an exceedingly difficult one. Many important theorems are stated without proof, and many details are left to the reader. I believe, however, that our account is full enough to serve as a guide to other mathematicians researching in this and allied subjects. Such readers will be familiar with Landau's Handbuch der Lehre con der Verteilung der Primzahlen, and will hardly need to be told how much we, in common with all other investigators in this field, owe to the writings and to the personal encouragement of its author.
G. H. H.
* * * * *
CONTENTS
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 Series
Bibliography
THE publication of this tract has been delayed by a variety of causes, and I am now compelled to issue it without Dr Riesz's help in the final correction of the proofs. This has at any rate, one advantage, that it gives me the opportunity of saying how conscious I am that whatever value it possesses is due mainly to his contributions to it, and in particular to the fact, that it contains the first systematic, account of his beautiful theory of the summation of series by 'typical means'.
The task of condensing any account of so extensive a theory into the compass of one of these tracts has proved an exceedingly difficult one. Many important theorems are stated without proof, and many details are left to the reader. I believe, however, that our account is full enough to serve as a guide to other mathematicians researching in this and allied subjects. Such readers will be familiar with Landau's Handbuch der Lehre con der Verteilung der Primzahlen, and will hardly need to be told how much we, in common with all other investigators in this field, owe to the writings and to the personal encouragement of its author.
G. H. H.
* * * * *
CONTENTS
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 Series
Bibliography
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The General Theory of Dirichlet's Series
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The General Theory of Dirichlet's Series
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Product Details
| ISBN-13: | 9781663552716 |
|---|---|
| Publisher: | Barnes & Noble Press |
| Publication date: | 08/18/2020 |
| Series: | Cambridge Tracts in Mathematics and Mathematical Physics , #18 |
| Pages: | 90 |
| Product dimensions: | 6.00(w) x 9.00(h) x 0.22(d) |
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