Exceptional Units and Numbers of Small Mahler Measure

DOI10.1080/10586458.1995.10504309zbMath0851.11064OpenAlexW2022168623MaRDI QIDQ4867495

Joseph H. Silverman

Publication date: 4 December 1996

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1062621144

zbMATH Keywords

cyclotomic polynomialexceptional unitssmall Mahler measure

Mathematics Subject Classification ID

Units and factorization (11R27) Algebraic number theory computations (11Y40) Exponential Diophantine equations (11D61) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Approximation to algebraic numbers (11J68)

Related Items

Small Salem numbers, exceptional units, and Lehmer's conjecture, SUMS OF POLYNOMIAL-TYPE EXCEPTIONAL UNITS MODULO, Polynomials with Restricted Coefficients and Prescribed Noncyclotomic Factors, The sums of exceptional units in a finite ring, On the sums of squares of exceptional units in residue class rings, 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, The unit equation over cyclic number fields of prime degree, Perturbing polynomials with all their roots on the unit circle, On the spectrum of the Zhang-Zagier height

Uses Software

• PARI/GP

Cites Work

• On equations in S-units and the Thue-Mahler equation
• The canonical height and integral points on elliptic curves
• Small Salem numbers
• Factorization of certain cyclotomic functions
• Counting points of small height on elliptic curves
• Algebraic integers whose conjugates lie near the unit circle
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer
• Unnamed Item