MathDB
Miklos Schweitzer 1976_5

Source: Sequences and Series

December 30, 2008
complex numbersreal analysisreal analysis unsolved

Problem Statement

Let S_{\nu}\equal{}\sum_{j\equal{}1}^n b_jz_j^{\nu} \;(\nu\equal{}0,\pm 1, \pm 2 ,...) , where the bj b_j are arbitrary and the zj z_j are nonzero complex numbers . Prove that ∣S0∣≤nmax⁡0<∣ν∣≤n∣Sν∣. |S_0| \leq n \max_{0<|\nu| \leq n} |S_{\nu}|. G. Halasz
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