TY - JOUR

T1 - Polynomial estimates, exponential curves and diophantine approximation

AU - Coman, Dan

AU - Poletsky, Evgeny A.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2010/11

Y1 - 2010/11

N2 - Let α ε (0,1)\ ℚ and K= ((ez, e αz: z ≤) ⊂ ℂ2 If P is a polynomial of degree n in ℂ2, normalized by ∥P∥k = 1,we obtain sharp estimates for ∥P∥Δ2 in terms of n, where Δ2 is the closed unit bidisk. For most α , we show that supP ∥P∥Δ2 2 log n). However, for in a subset S of the Liouville numbers, supP ∥P∥Δ2 has bigger order of growth. We giveaprecise characterization of the set S and study its properties.

AB - Let α ε (0,1)\ ℚ and K= ((ez, e αz: z ≤) ⊂ ℂ2 If P is a polynomial of degree n in ℂ2, normalized by ∥P∥k = 1,we obtain sharp estimates for ∥P∥Δ2 in terms of n, where Δ2 is the closed unit bidisk. For most α , we show that supP ∥P∥Δ2 2 log n). However, for in a subset S of the Liouville numbers, supP ∥P∥Δ2 has bigger order of growth. We giveaprecise characterization of the set S and study its properties.

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U2 - 10.4310/MRL.2010.v17.n6.a11

DO - 10.4310/MRL.2010.v17.n6.a11

M3 - Article

AN - SCOPUS:78149443325

VL - 17

SP - 1125

EP - 1136

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 6

ER -