THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

DOI10.1017/S1446788711001030zbMath1290.11143MaRDI QIDQ3173414

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Publication date: 10 October 2011

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

LLL algorithmsemi-infinite linear programmingSalem numberabsolute traceexplicit auxiliary functiontotally positive algebraic integer

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Algebraic number theory computations (11Y40) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (18)

Salem numbers with minimal trace ⋮ The size of algebraic integers with many real conjugates ⋮ The absolute trace of totally positive reciprocal algebraic integers ⋮ Algebraic integers with small potential energy ⋮ THE ABSOLUTE -MEASURE OF TOTALLY POSITIVE ALGEBRAIC INTEGERS ⋮ An analog to the Schur-Siegel-Smyth trace problem ⋮ Retracted: A generalization of the Schur-Siegel-Smyth trace problem ⋮ The S-measure for algebraic integers having all their conjugates in a sector ⋮ Pre-modular fusion categories of global dimension \(p^2\) ⋮ A trace bound for positive definite connected integer symmetric matrices ⋮ Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8 ⋮ The absolute trace of totally positive algebraic integers ⋮ Estimates for the number of rational points on simple abelian varieties over finite fields ⋮ A variant \(S_2\) measure for algebraic integers all of whose conjugates Lie in a sector ⋮ Finding all Salem numbers of trace \(-1\) and degree up to 20 ⋮ Totally positive algebraic integers with small trace ⋮ Weil numbers in finite extensions of ℚ^{𝕒𝕓}: the Loxton-Kedlaya phenomenon ⋮ Seventy years of Salem numbers

Cites Work

• Unnamed Item
• Totally positive algebraic integers of small trace
• Inequalities on the Mahler measure of a polynomial
• The trace of totally positive and real algebraic integers
• Trace of totally positive algebraic integers and integer transfinite diameter
• On integer Chebyshev polynomials
• Computing totally positive algebraic integers of small trace
• On the smallest value of the maximal modulus of an algebraic integer
• THERE ARE SALEM NUMBERS OF EVERY TRACE
• On the linear independence measure of logarithms of rational numbers
• Salem numbers of negative trace
• Integer transfinite diameter and polynomials with small Mahler measure

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