TY - JOUR
T1 - Polynomial estimates, exponential curves and diophantine approximation
AU - Coman, Dan
AU - Poletsky, Evgeny A.
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
SN - 1073-2780
VL - 17
SP - 1125
EP - 1136
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 6
ER -