A note on a theorem of Daboussi期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A note on a theorem of Daboussi

Authors:	K.-H. Indlekofer I. Kátai

Affiliation:	1. Universit?t Paderborn, D-33098, Paderborn, Warburger Str. 100 2. Department Of Computer Algebra, E?tv?s Loránd University, H-1117, Budapest, Pázmány Péter Sétány 1/C

Abstract:	The following assertion is proved. Let $mathcal{N}_k$ be the set of integers the number of the prime power of which is . Let ${pi }_k left( x right)$ be the size of $mathcal{N}_k bigcap {left[ {1,x} right]}$ . Then for each irrational , uniformly in $left( {0 < } right)delta < tfrac{k}{{{text{loglog}};x}} < 2 - delta$ , begin{equation} frac{1}{pi_k(x)} bigg\|sum _{alul{nle x}{nincN_k}} f(n) e^{2pi inalpha}bigg\|to 0, end{equation} where is an arbitrary multiplicative function with , is a positive constant. This revised version was published online in June 2006 with corrections to the Cover Date.

Keywords:	exponential sums multiplicative functions
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