Small Salem numbers, exceptional units, and Lehmer's conjecture

DOI10.1216/rmjm/1181072040zbMath0883.11045OpenAlexW2070502217WikidataQ123298301 ScholiaQ123298301MaRDI QIDQ1359154

Joseph H. Silverman

Publication date: 5 March 1998

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/vol26-3/contents/contents.htm

zbMATH Keywords

Mahler measureLehmer conjectureSalem numberalgebraic numberexceptional unitabsolute canonical height

Mathematics Subject Classification ID

Units and factorization (11R27) Exponential Diophantine equations (11D61) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Approximation to algebraic numbers (11J68)

Related Items

SUMS OF POLYNOMIAL-TYPE EXCEPTIONAL UNITS MODULO ⋮ On the sumsets of polynomial units in a finite commutative ring ⋮ The sums of exceptional units in a finite ring ⋮ On the sums of squares of exceptional units in residue class rings ⋮ The arithmetic and geometry of Salem numbers ⋮ On the sumsets of exceptional units in \(\mathbb {Z}_n\) ⋮ On a question of \(f\)-exunits in \(\mathbb{Z}/n\mathbb{Z} \) ⋮ On sums of polynomial-type exceptional units in \(\mathbb{Z}/n\mathbb{Z}\) ⋮ Sums of exceptional units in residue class rings ⋮ Seventy years of Salem numbers

Cites Work

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• On equations in S-units and the Thue-Mahler equation
• Lower bounds for heights on elliptic curves
• Small Salem numbers
• Factorization of certain cyclotomic functions
• A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan
• Algebraic integers whose conjugates lie in the unit circle
• On a question of Lehmer and the number of irreducible factors of a polynomial
• Counting points of small height on elliptic curves
• Algebraic integers whose conjugates lie near the unit circle
• Exceptional Units and Numbers of Small Mahler Measure
• Algebraic integers near the unit circle
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer