asymptotic formulae for sums of reciprocals of arithmetical functions and related results /
J.-M. de Koninck and A. Ivić.
2nd ed.
New York :
sole distributors for the U.S.A. and Canada, Elsevier North-Holland,
1980.
1 online resource (281 p.).
North-Holland mathematics studies ;
Notas de matemática ;
43
72
Description based upon print version of record.
Includes bibliographical references and index.
Front Cover; Topics in Arithmetical Functions; Copyright Page; Table of Contents; Introduction; Notation; Chapter 1. Reciprocals of multiplicative functions; 1. Notes; Chapter 2. Reciprocals of ""small"" additive functions; 1. Introduction; 2. The method; 3. Selberg's result and basic definitions; 4. The main theorem; 5. Applications of the main theorem; 6. A generalization of the main theorem; 7. Estimates for ? 1/((n))k for an arbitrary positive n.x; Notes; Chapter 3. Reciprocals of logarithms of multiplicative functions; 1. Functions with main term asymptotic to Cx/logx
2. Functions with main term asymptotic to Cx/log logx 3. Functions with main term asymptotic to Cx; 4.Notes; Chapter 4. Suns of quotients of additive functions; 1. Introduction; 2. Sums of quotients of ""small"" additive functions; 3. Sums of qwtients of additive functions which behave ""like c log n""; Notes; Chapter 5. A sharpening of asymptotic formulae; 1. Introduction; 2. The lemmas; 3. The theorems; 4. Applications and remarks; Notes; Chapter 6. Reciprocals of ""large"" additive functions; 1. Introduction; 2. Bounds for sums of reciprocals