The Distribution of Integers in a Totally Real Cubic Field
Number Theory
2016-06-14 v1
Abstract
Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of given trace in a general totally real number field of any degree. When the field is cubic, we show that the asymptotic behavior of a weighted Diophantine sum is related to the structure of the unit group. The main term can be expressed in terms of Gr\"ossencharacter -functions.
Keywords
Cite
@article{arxiv.1606.04049,
title = {The Distribution of Integers in a Totally Real Cubic Field},
author = {Tianyi Mao},
journal= {arXiv preprint arXiv:1606.04049},
year = {2016}
}