On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions

On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions

The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.

On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions

Coherence for Tricategories

This work defines the concept of tricategory as the natural 3-dimensional generalization of bicategory. Trihomomorphism and triequivalence for tricategories are also defined so as to extend the concepts of homomorphism and biequivalence for bicategories.