English

On the magnitudes of some small cyclotomic integers

Number Theory 2012-06-19 v1

Abstract

We prove the last of five outstanding conjectures made by R.M. Robinson from 1965 concerning small cyclotomic integers. In particular, given any cyclotomic integer β\beta all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value one of four explicit types given by two infinite classes and two exceptional cases. We also extend this result by showing that with the addition of one form, the conjecture is true for β\beta with magnitudes up to 5+1/25.

Keywords

Cite

@article{arxiv.1206.3598,
  title  = {On the magnitudes of some small cyclotomic integers},
  author = {Frederick Robinson and Michael Wurtz},
  journal= {arXiv preprint arXiv:1206.3598},
  year   = {2012}
}