摘要
Suppose x is a positive number large enough, α and R are real numbers satisfying 0≤α【1 and 1≤R【x. Let L(x; R, α) denote the number of solutions of the inequality α≤{x/n}【α+R/n,n≤x. (1) It is an extention of the Dirichlet divisor problem to the estimation of L(x;R,α).It was conjectured that L(x; R, α)(?)Rx~ε (2) holds uniformly for 0≤α【1. But the results at present are far from this ideal result.
基金
Project supported by the National Natural Science Foundation of China.
