A generalization of the Schur-Siegel-Smyth trace problem

Kyle Pratt, George Shakan, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Let α be a totally positive algebraic integer, and define its absolute trace to be Tr(α)deg(α), the trace of α divided by the degree of α. Elementary considerations show that the absolute trace is always at least one, while it is plausible that for any ε > 0, the absolute trace is at least 2. ε with only finitely many exceptions. This is known as the Schur-Siegel-Smyth trace problem. Our aim in this paper is to show that the Schur-Siegel-Smyth trace problem can be considered as a special case of a more general problem.

Original languageEnglish (US)
Pages (from-to)489-500
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume436
Issue number1
DOIs
StatePublished - Apr 1 2016

Keywords

  • Minimal polynomial
  • Schur-Siegel-Smyth trace problem
  • Totally positive algebraic number

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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