The General Theory of Dirichlet's Series,9780486446578

The General Theory of Dirichlet's Series

by ;
ISBN13: 9780486446578
ISBN10: 0486446573
Format: Hardcover
Pub. Date: 2005-11-14
Publisher(s): Dover Publications
List Price: $30.00

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Summary

This classic work, written by two of the twentieth century's most distinguished mathematicians, 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. Topics include the elementary theory of the convergence of Dirichlet's series; the formula for the sum of the coefficients of a Dirichlet's series; the summation of series by typical means and general arithmetic theorems concerning typical means; Abelian and Tauberian theorems; and the multiplication of Dirichlet's series. 1915 ed.

Table of Contents

I. INTRODUCTION 1(2)
II. ELEMENTARY THEORY OF THE CONVERGENCE OF DIRICHLET'S SERIES 3(8)
III. THE FORMULA FOR THE SUM OF THE COEFFICIENTS OF A DIRICHLET'S SERIES: THE ORDER OF THE FUNCTION REPRESENTED BY THE SERIES 11(8)
IV. THE SUMMATION OF SERIES BY TYPICAL MEANS 19(7)
V. GENERAL ARITHMETIC THEOREMS CONCERNING TYPICAL MEANS 26(13)
VI. ABELIAN AND TAUBERIAN THEOREMS. 39(10)
VII. FURTHER DEVELOPMENTS OF THE THEORY OF FUNCTIONS REPRESENTED BY DIRICHLET'S SERIES 49(12)
VIII. THE MULTIPLICATION OF DIRICHLET'S SERIES 61(8)
BIBLIOGRAPHY 69

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