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arXiv · 1611.07287

The Norm of Gaussian Periods

P. Habegger
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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.

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P. Habegger. 2016-11-22. The Norm of Gaussian Periods. https://arxiv.org/abs/1611.07287

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