On the mean square of the error term for the asymmetric two-dimensional divisor problem (I)
β Scribed by Wenguang Zhai; Xiaodong Cao
- Publisher
- Springer Vienna
- Year
- 2008
- Tongue
- English
- Weight
- 267 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0026-9255
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π SIMILAR VOLUMES
Let (x) be the error term in the Dirichlet divisor problem. The purpose of this paper is to study the difference between two kinds of mean value formulas of (x), that is, the mean value formulas x 1 (u) k du and n x (n) k with a natural number k. In particular we study the case k = 2 and 3 in detail
The arithmetic function r & k (n) counts the number of ways to write a natural number n as the difference of two kth powers (k 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of r & k (n) leads in a natural way to a certain error term 2 & k (t). In this ar