Let F_(p.t)(n) denote the number of the coefficients of (x_1+x_2+…+x_t)~j. 0≤j≤n-1, which are not divisible by the prime p. Define G_(p.t)(n)=F_(p.t)(n)/n~θ and β(p.t)=lim inf F_(p.t)(n)/n~θ, where θ=(log(p+t-1...Let F_(p.t)(n) denote the number of the coefficients of (x_1+x_2+…+x_t)~j. 0≤j≤n-1, which are not divisible by the prime p. Define G_(p.t)(n)=F_(p.t)(n)/n~θ and β(p.t)=lim inf F_(p.t)(n)/n~θ, where θ=(log(p+t-1 t))/(logp). In this paper, we mainly prove that G_(p.t) can be extended to a continuous function on R^+, and the function G_(p.t) is nowhere monotonic. Both the set of differential points of the function G_(p.t) and the set of non-differential points of the function G_(p.t) are dense in R^+.展开更多
基金Supported by the National Natural Science Foundation of China. Grant No. 10171046 and the "333 Project" Foundation of Jiangsu Province of China.
文摘Let F_(p.t)(n) denote the number of the coefficients of (x_1+x_2+…+x_t)~j. 0≤j≤n-1, which are not divisible by the prime p. Define G_(p.t)(n)=F_(p.t)(n)/n~θ and β(p.t)=lim inf F_(p.t)(n)/n~θ, where θ=(log(p+t-1 t))/(logp). In this paper, we mainly prove that G_(p.t) can be extended to a continuous function on R^+, and the function G_(p.t) is nowhere monotonic. Both the set of differential points of the function G_(p.t) and the set of non-differential points of the function G_(p.t) are dense in R^+.
