Open AccessOn the conjugates of certain algebraic integers
Author(s) -
Toufik Zaı̈mi
Publication year - 2016
Publication title -
publications de l institut mathematique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim1613281z
Subject(s) - mathematics , conjugate , algebraic number , combinatorics , natural number , field (mathematics) , discrete mathematics , pure mathematics , mathematical analysis
A well-known theorem, due to C. J. Smyth, asserts that two conjugates of a Pisot number, having the same modulus are necessary complex conjugates. We show that this result remains true for K-Pisot numbers, where K is a real algebraic number field. Also, we prove that a j-Pisot number, where j is a natural number, can not have more than 2j conjugates with the same modulus.
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