ON SOME GENERALIZATIONS OF MEAN VALUE THEOREMS FOR ARITHMETIC FUNCTIONS OF TWO VARIABLES
Let be an arithmetic function of two variables. We study the existence of the limit:
where kis a fixed positive integer. Moreover, we express this limit as an infinite product over all prime numbers in the case that fis a multiplicative function of two variables. This study is a generalization of Cohen-van der Corput’s results to the case of two variables.
asymptotic results, arithmetic functions.
