Publications [#302456] of Lillian B. Pierce

Papers Published

1. Heath-Brown, DR; Pierce, LB, Counting rational points on smooth cyclic covers, Journal of Number Theory, vol. 132 no. 8 (2012), pp. 1741-1757, Elsevier BV, ISSN 0022-314X [doi]
   (last updated on 2024/04/24)

   Abstract:
   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.