The General Theory of Dirichlet's Series by G.H. Hardy, Marcel Riesz
About this book :-
"The General Theory of Dirichlet's Series" by "G. H. Hardy" and Marcel Riesz is a foundational text in "analytic number theory". First published in 1915, the book introduces Dirichlet series, these series are essential tools in understanding the distribution of prime numbers and play a central role in the study of L-functions.
The book explores the convergence, analytic continuation, and functional properties of Dirichlet series. Hardy and Riesz present rigorous methods for analyzing these series, including Abelian and Tauberian theorems, which link the behavior of a series at its boundary to its behavior within the convergence domain. Their systematic approach makes complex concepts in infinite series and complex analysis more accessible to advanced students and researchers.
Recognized as a classic in mathematics, "The General Theory of Dirichlet's Series" remains a key reference for mathematicians studying the analytical aspects of number theory. The clear exposition and depth of content by "G. H. Hardy" and Riesz have ensured the book’s lasting impact, providing essential insights for understanding the structure and behavior of Dirichlet series.
Book Detail :-
Title:
The General Theory of Dirichlet's Series by G.H. Hardy, Marcel Riesz
Publisher:
Cambridge University Press
Year:
1915
Pages:
95
Type:
PDF
Language:
English
ISBN-10 #:
1532868758, B00A44MFKK
ISBN-13 #:
N\A
License:
Public Domain Work
Amazon:
Amazon
About Author :-
The author
G.H. Hardy
(1877–1947) was a renowned British mathematician, famous for his work in "analytic number theory" and "Dirichlet series". A professor at Cambridge University, he emphasized rigor, elegance, and the beauty of mathematics for its own sake. Hardy is also celebrated for his collaboration with Srinivasa Ramanujan, producing groundbreaking results in number theory and mathematical functions. He co-authored "The General Theory of Dirichlet's Series" with Marcel Riesz, a seminal work exploring the convergence, properties, and applications of "Dirichlet series". Hardy’s focus on precision and clarity made the book a lasting reference in mathematics and a foundation for modern research.
Book Contents :-
1. Introduction
2. Elementary Theory of the Convergence of Dirichlet's Series
3. The Formula for the Sum of the Coefficients of a Dirichlet's Series: The Order of the Function Represented by the Series
4. The Summation of Series of Typical Means
5. General Arithmetic Theorems Concerning Typical Means
6. Abelian and Tauberian Theorems
7. Further Developements of the Theory of Functions Represented by Dirichlet's Series
8. The Multiplication of Dirichlet's Series
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