MathDB
Miklos Schweitzer 1968_5

Source:

October 8, 2008
inequalitiesreal analysisreal analysis unsolved

Problem Statement

Let k k be a positive integer, z z a complex number, and ε<12 \varepsilon <\frac12 a positive number. Prove that the following inequality holds for infinitely many positive integers n n: ∣∑0≤l≤nk+1(n−kll)zl∣≥(12−ε)n. \mid \sum_{0\leq l \leq \frac{n}{k+1}} \binom{n-kl}{l}z^l \mid \geq (\frac 12-\varepsilon)^n. P. Turan
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