On a generalized divisor problem II

Author:

Lau Yuk-Kam

Abstract

AbstractWe investigate the Ω±-result of Δa(x) and its number of sign-changes in an interval [1, T], denoted by Xa(T), for -1 ≤ a < -1/2. We can prove that TaXa(T) which is the best possible in order of magnitude.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference9 articles.

1. Pétermann Y.-F. S. , About a Theorem of Paolo Codecà’s and Omega Estimates for Arithmetical Convolutions, Second Part, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 17 (1990), 343–353.

2. On the limiting distribution of a generalized divisor problem for the case -1≤a<-1/2

3. Lau Y.-K. , On a generalized divisor problem I, Nagoya Math. J., 165 (2002), 71–78.

4. Pétermann Y.-F. S. , On the distribution of values of an error term related of the Euler functions, Théorie des nombres, (Quebec, PQ, 1987), de Gruyter, Berlin (1989), pp. 785–797.

5. Pétermann Y.-F. S. , Changes of sign of error terms related to Euler’s function and to divisor functions, Comm. Math. Helv., 61 (1986), 84–101.

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