On the magnitudes of some small cyclotomic integers

Frederick Robinson, and Michael Wurtz. "On the magnitudes of some small cyclotomic integers." Acta Arithmetica 160.4 (2013): 317-332. <http://eudml.org/doc/286111>.

@article{FrederickRobinson2013,
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 all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of 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 with magnitudes up to 5 + 1/25.},
author = {Frederick Robinson, Michael Wurtz},
journal = {Acta Arithmetica},
keywords = {small cyclotomic integer; house},
language = {eng},
number = {4},
pages = {317-332},
title = {On the magnitudes of some small cyclotomic integers},
url = {http://eudml.org/doc/286111},
volume = {160},
year = {2013},
}

TY - JOUR
AU - Frederick Robinson
AU - Michael Wurtz
TI - On the magnitudes of some small cyclotomic integers
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 4
SP - 317
EP - 332
AB - 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 all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of 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 with magnitudes up to 5 + 1/25.
LA - eng
KW - small cyclotomic integer; house
UR - http://eudml.org/doc/286111
ER -