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Arithmetical Functions (Paperback, 1970 ed.)
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Arithmetical Functions (Paperback, 1970 ed.)
Series: Grundlehren der mathematischen Wissenschaften, 167
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The plan of this book had its inception in a course of lectures on
arithmetical functions given by me in the summer of 1964 at the
Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of
Technology, Zurich, at the invitation of Professor Beno Eckmann. My
Introduction to Analytic Number Theory has appeared in the
meanwhile, and this book may be looked upon as a sequel. It
presupposes only a modicum of acquaintance with analysis and number
theory. The arithmetical functions considered here are those
associated with the distribution of prime numbers, as well as the
partition function and the divisor function. Some of the problems
posed by their asymptotic behaviour form the theme. They afford a
glimpse of the variety of analytical methods used in the theory,
and of the variety of problems that await solution. I owe a debt of
gratitude to Professor Carl Ludwig Siegel, who has read the book in
manuscript and given me the benefit of his criticism. I have
improved the text in several places in response to his comments. I
must thank Professor Raghavan Narasimhan for many stimulating
discussions, and Mr. Henri Joris for the valuable assistance he has
given me in checking the manuscript and correcting the proofs. K.
Chandrasekharan July 1970 Contents Chapter I The prime number
theorem and Selberg's method 1. Selberg's fonnula . . . . . . 1 2.
A variant of Selberg's formula 6 12 3. Wirsing's inequality . . . .
. 17 4. The prime number theorem. ."
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