The Norm of Gaussian Periods
Number Theory
2016-11-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1611.07287,
title = {The Norm of Gaussian Periods},
author = {P. Habegger},
journal= {arXiv preprint arXiv:1611.07287},
year = {2016}
}