Geodesic
On the magnitudes of some small cyclotomic integers
Frederick Robinson 1   ; Michael Wurtz 2
1 Department of Mathematics, UCLA Box 951555 Los Angeles, CA, U.S.A.
2 Microsoft Corporation 1 Microsoft Way miwurtz 36/3511 Redmond, WA 98052, U.S.A.
Acta Arithmetica, Tome 160 (2013) no. 4, pp. 317-332 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\beta $ 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 $\beta $ with magnitudes up to $5+ {1/25}$.
DOI : 10.4064/aa160-4-2
Keywords: prove five outstanding conjectures made robinson concerning small cyclotomic integers particular given cyclotomic integer beta whose conjugates have absolute value nbsp prove largest conjugate has absolute value explicit types given infinite classes exceptional cases extend result showing addition form conjecture beta magnitudes

Frederick Robinson  1   ; Michael Wurtz  2

1 Department of Mathematics, UCLA Box 951555 Los Angeles, CA, U.S.A.
2 Microsoft Corporation 1 Microsoft Way miwurtz 36/3511 Redmond, WA 98052, U.S.A. 
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Frederick Robinson; Michael Wurtz. On the magnitudes of some small cyclotomic integers. Acta Arithmetica, Tome 160 (2013) no. 4, pp. 317-332. doi: 10.4064/aa160-4-2

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