New estimates in the four-dimensional divisor problem with applications |
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Authors: | E. Krätzel |
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Affiliation: | 1.Institut für Mathematik,Universit?t Wien,Wien,Austria |
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Abstract: | In this article we consider three problems: 1. The asymptotic behaviour of the quadratic moment of the exponential divisor function. 2. The distribution of powerful integers of type 4. 3. The average number of direct factors of a finite Abelian group. We prove new estimates for the error terms in the asymptotic representations. For this purpose new estimates in the general four-dimensional divisor problem are needed. |
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