On the divisor function in short intervals

摘要

Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formula lllå_{x < n £ x+h(x)}d(n) ~ h(x)logxbegin{array}{lll}sum limits_{x < n leq x+h(x)}d(n)sim h(x)log xend{array}