Local Distribution of Ordered Factorizations of Integers Original Research Article

Denote am(n)=∑n1…nm=n; n1, …, nmgreater-or-equal, slanted2 1 to be the number of ordered factorizations of an integer n into m factors. We are concerned with the local distribution A(x, m)= ∑nless-than-or-equals, slantx am(n). A recent work of Hwang studied A(x, m) by using two methods: the analytic method and saddle-point method. Hwang then concluded a simple asymptotic formula for m=o((log x)2/3). We prove here that the analytic method is in fact sufficient to yield this formula, and moreover, give some refinements.