Counting rational points on smooth cyclic covers

Details Counting rational points on smooth cyclic covers Counting rational points on smooth cyclic covers

2011-09-07

arxiv.org/abs/1109.1455v1

Mathematics

Number Theory

Scientific paper

A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space P^{n-1}. In this paper, we achieve Serre's conjecture in the special case of smooth cyclic covers of any degree when n is at least 10, and surpass it for covers of degree 3 or higher 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.

Affiliated with

Also associated with

No associations

Rating

Counting rational points on smooth cyclic covers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting rational points on smooth cyclic covers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting rational points on smooth cyclic covers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-306370