Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

R. G. Nath


R. G. Nath


Quite frequently in the study of number theory we become acquainted with special functions which are defined on the set of positive integers. These functions are known as Number-theoretic functions or Arithmetical functions. This report will give some of the general ideas of the multipli­cative number-theoretic functions.

The first part of this report will be devoted to the general develop­ment of such functions by means of definitions and theorems. The second part will consist of generalizations of a particular function, the -r-function.

Throughout this paper, lower case Greek letters will represent real numbers and lower case English letters will represent integers. Also the basic ideas of summation and product will be assumed as already familiar to the reader.