Local distribution of ordered factorizations of integers

[摘要] Denote am (n) = [GRAPHICS] 1 to bethe number of ordered factorizations of an integer n into m factors. We are concerned with the local distribution A(x,m) = Sigma(n less than or equal to x) a(m)(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. (C) 2001 Elsevier Science.

[发布日期] 2001-12-01