Introduction to Arithmetical Functions

1. Front Matter

   Pages i-vii

   PDF

2. Multiplicative Functions

   • Paul J. McCarthy

   Pages 1-69

3. Ramanujan Sums

   • Paul J. McCarthy

   Pages 70-113

4. Counting Solutions of Congruences

   • Paul J. McCarthy

   Pages 114-148

5. Generalizations of Dirichlet Convolution

   • Paul J. McCarthy

   Pages 149-183

6. Dirichlet Series and Generating Functions

   • Paul J. McCarthy

   Pages 184-254

7. Asymptotic Properties of Arithmetical Functions

   • Paul J. McCarthy

   Pages 255-292

8. Generalized Arithmetical Functions

   • Paul J. McCarthy

   Pages 293-332

9. Back Matter

   Pages 333-365

   PDF

The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.

• Counting
• Functions
• Ramanujan
• approximation
• arithmetic
• congruence
• convolution
• form
• function
• information
• set

• Department of Mathematics, University of Kansas, Lawrence, USA

  Paul J. McCarthy