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The Norm of Gaussian Periods (2018)

Habegger P.

Oxford University Press

In: Quarterly Journal of Mathematics

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Publication Date: 2018-03-06

Description: 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 prove a case of Myerson’s Conjecture for periods of arbitrary odd length and provide a rate of convergence. Our method involves a result of Bombieri et al . 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.

Print ISSN: 0033-5606

Electronic ISSN: 1464-3847

Topics: Mathematics

Published by Oxford University Press

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