Computing totally positive algebraic integers of small trace

Author:
James McKee

Journal:
Math. Comp. **80** (2011), 1041-1052

MSC (2010):
Primary 11R04, 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-2010-02424-X

Published electronically:
October 22, 2010

Table supplement:
Some minimal trace totally positive algebraic integers (PDF)

MathSciNet review:
2772109

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct minimal polynomials of totally positive algebraic integers of small absolute trace by consideration of their reductions modulo auxiliary polynomials. Many new examples of such polynomials of minimal absolute trace (for given degree) are found. The computations are pushed to degrees that previously were unattainable, and one consequence is that the new examples form the majority of all those known. As an application, we produce a new bound for the Schur-Siegel-Smyth trace problem.

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Additional Information

**James McKee**

Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, England, United Kingdom

Email:
james.mckee@rhul.ac.uk

Received by editor(s):
December 23, 2009

Received by editor(s) in revised form:
February 22, 2010

Published electronically:
October 22, 2010

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.