摘要
讨论有关素因子函数在小区间上的均值性质,通过与Riemannξ-函数的零点间的关系,得到的一个渐近估计,从而给出P(n),P(n)/P(n),A(n)/ω(n)和B(n)/Ω(n)等函数在小区间[x,x+y]上的均值估计.
Mean value estimaties are discussed for some arithmetic functions of prime factors of an integer in short interval. According to relation between and zeros of Riemann ζ-function,there is an estimate of that mean value estimates of P(n),and in interval (x,x+y) are given.Theorem 1 Let cn(n≥1) be real,andbe absolutely convergent for Re(s)>1,a constant of satisfiesthen there is c=c(A) for any A>0,is true uniformly forTheorem 2 There is c=c(A) for any A>0,are thue unifrmly for.Similar results are true for
出处
《山东大学学报(理学版)》
CAS
CSCD
1995年第1期1-7,共7页
Journal of Shandong University(Natural Science)
关键词
素因子
小区间
均值估计
prime factor
short interval
mean value estimate