Flat Polynomials on the Unit Circle—note on a Problem of Littlewood
نویسنده
چکیده
In [10], Littlewood conjectured that there are positive absolute constants Ax and A2 such that, for arbitrarily large n, one can find anfne^n or a gn€%, such that A.Vin+l) < \fM\ < A2V("+V (1-1) or ^ V ( « + l ) < \gn(0)\<A2V(n+\) (1.2) for all 6. The weaker conjecture (1.2) has been solved by Korner [9] (using a construction of Byrnes [6]) in the affirmative. Soon after this breakthrough, Kahane [8] produced polynomials gn £ Sn with the even more striking property ,. maxg|gn(6)| limra—:—:—— = 1 (1.3) minjg(^)|
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تاریخ انتشار 2006