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Asymptotics for a class of arithmetic functions

Wenguang Zhai — 2015

Acta Arithmetica

We study the asymptotic behaviour of the summatory function of a class of arithmetic functions. These functions are generalizations of the well-known general 4-dimensional divisor function d₄(n). We show that the corresponding error estimate is the best one can obtain by the present methods of analytic number theory.

On the distribution of p α modulo one

Xiaodong CaoWenguang Zhai — 1999

Journal de théorie des nombres de Bordeaux

In this paper, we give a new upper-bound for the discrepancy D ( N ) : = sup 0 γ 0 | p / N p α γ 1 - π ( N ) γ | for the sequence ( p α ) , when 5 / 3 α > 3 and α 2 .

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