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THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

Published online by Cambridge University Press:  17 February 2011

YANHUA LIANG
Affiliation:
Department of Mathematics, Southwest University of China, 2 Tiansheng Road Beibei, 400715 Chongqing, PR China (email: [email protected])
QIANG WU*
Affiliation:
Department of Mathematics, Southwest University of China, 2 Tiansheng Road Beibei, 400715 Chongqing, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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Let α be a totally positive algebraic integer of degree d≥2 and α1=α,α2,…,αd be all its conjugates. We use explicit auxiliary functions to improve the known lower bounds of Sk/d, where Sk=∑ di=1αki and k=1,2,3. These improvements have consequences for the search of Salem numbers with negative traces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The corresponding author was supported by the Natural Science Foundation of Chongqing grant CSTC no. 2008BB0261.

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