2016/11/22 by Habegger, P.
#05A15 #11J71 #11K60 #11R06 (Primary) #37A45 (Secondary) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1611.07287
Gaussian periods are cyclotomic integers with a long history in number theory and connections to problems in combinatorics. We investigate the asymptotic behavior of the absolute norm of a Gaussian period and provide a rate of convergence in a case of Myerson's Conjecture for periods of arbitrary odd length. Our method involves a result of Bombieri, Masser, and Zannier on unlikely intersections in the algebraic torus as well as work of the author on the diophantine approximations to a set definable in an o-minimal structure. In the appendix we make a result of Lawton on Mahler measures quantitative.