The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><...The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><sup>c<sub>1</sub></sup>]=…[n<sub>k</sub><sup>c<sub>k</sub></sup>], where 1【c<sub>1</sub>【…【c<sub>k</sub> are fixed constants. It is proved that π（x; c<sub>1</sub>, …, c<sub>k</sub>） has an asymptotic formula if c<sub>1</sub><sup>-1</sup>+ …+c<sub>k</sub><sup>-1</sup>】k-k/（4k<sup>2</sup>+2）.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801021)the Natural Science Foundation of Shandong Province (Grant No. Q98A02110).
文摘The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><sup>c<sub>1</sub></sup>]=…[n<sub>k</sub><sup>c<sub>k</sub></sup>], where 1【c<sub>1</sub>【…【c<sub>k</sub> are fixed constants. It is proved that π（x; c<sub>1</sub>, …, c<sub>k</sub>） has an asymptotic formula if c<sub>1</sub><sup>-1</sup>+ …+c<sub>k</sub><sup>-1</sup>】k-k/（4k<sup>2</sup>+2）.
