On the Conjecture of Lehmer, Limit Mahler Measure of Trinomials and Asymptotic Expansions

DOI10.1515/udt-2016-0006zbMath1455.11143OpenAlexW2578619400WikidataQ123221518 ScholiaQ123221518MaRDI QIDQ2835462

Jean-Louis Verger-Gaugry

Publication date: 2 December 2016

Published in: Uniform distribution theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/udt-2016-0006

zbMATH Keywords

asymptotic expansiondivergent seriesMahler measurePisot numbertrinomialdiscrepancy functionPerron numberSchinzel-Zassenhaus conjectureBoyd conjectureErdős-Turán-Mignotte-AmorosoLehmer Conjecturelimit equidistributionLind- -Boyd conjectureSmyth conjecture

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials (irreducibility, etc.) (11R09) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Irregularities of distribution, discrepancy (11K38)

Related Items (4)

On a class of lacunary almost Newman polynomials modulo \(p\) and density theorems ⋮ Properties of trinomials of height at least \(2\) ⋮ Alphabets, rewriting trails and periodic representations in algebraic bases ⋮ On the reducibility and the lenticular sets of zeroes of almost Newman lacunary polynomials

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