
Counting rational points on smooth cyclic covers
Publication
, Journal Article
Heath-Brown, DR; Pierce, LB
Published in: Journal of Number Theory
2012
A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space Pn-1. In this paper, we achieve Serre's conjecture in the special case of smooth cyclic covers of any degree when n≥ 10, and surpass it for covers of degree r≥ 3 when n> 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsingular leading form, obtained via a combination of an r-th power sieve and the q-analogue of van der Corput's method. © 2012 Elsevier Inc.
Duke Scholars
Published In
Journal of Number Theory
DOI
ISSN
0022-314X
Publication Date
2012
Volume
132
Issue
8
Start / End Page
1741 / 1757
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Heath-Brown, D. R., & Pierce, L. B. (2012). Counting rational points on smooth cyclic covers. Journal of Number Theory, 132(8), 1741–1757. https://doi.org/10.1016/j.jnt.2012.02.010
Heath-Brown, D. R., and L. B. Pierce. “Counting rational points on smooth cyclic covers.” Journal of Number Theory 132, no. 8 (2012): 1741–57. https://doi.org/10.1016/j.jnt.2012.02.010.
Heath-Brown DR, Pierce LB. Counting rational points on smooth cyclic covers. Journal of Number Theory. 2012;132(8):1741–57.
Heath-Brown, D. R., and L. B. Pierce. “Counting rational points on smooth cyclic covers.” Journal of Number Theory, vol. 132, no. 8, 2012, pp. 1741–57. Scival, doi:10.1016/j.jnt.2012.02.010.
Heath-Brown DR, Pierce LB. Counting rational points on smooth cyclic covers. Journal of Number Theory. 2012;132(8):1741–1757.

Published In
Journal of Number Theory
DOI
ISSN
0022-314X
Publication Date
2012
Volume
132
Issue
8
Start / End Page
1741 / 1757
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics