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On the magnitudes of some small cyclotomic integers

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Robinson F., Wurtz M.

Acta Arithmetica

2013

tom 160

nr 4

317-332

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.

Ograniczanie wyników

1 Acta Arithmetica

1 Robinson F.

1 Wurtz M.

1 2013

Wyniki wyszukiwania

On the magnitudes of some small cyclotomic integers