On the k-dimensional Piatetski-Shapiro prime number theorem

Authors
Zhai, WG
Citation
Wg. Zhai, On the k-dimensional Piatetski-Shapiro prime number theorem, SCI CHINA A, 42(11), 1999, pp. 1173-1183
Citations number
10
Categorie Soggetti
Multidisciplinary
Journal title
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN journal
10016511 → ACNP
Volume
42
Issue
11
Year of publication
1999
Pages
1173 - 1183
Database
ISI
SICI code
1001-6511(199911)42:11<1173:OTKPPN>2.0.ZU;2-I
Abstract
The k-dimensional Piatetski-Shapiro prime number problem for k greater than or equal to 3 is studied. Let pi(x(i)c(1),(...),c(kappa)) denote the numbe r of primes p with p less than or equal to x, p = [n(1)(c1)] = [ n(k)(ck)], where 1 < c(1) <(...)< c(k) are fixed constants. It is proved that pi(x; c (1),(...),c(k)) has an asymptotic formula if c(1)(-1) +(...)+ c(k)(-1) > k - k/(4k(2) + 2).