Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed...Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+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Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).
