Journal of the Ramanujan Mathematical Society

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Complete Uniform Distribution of Some Oscillating Sequences


Affiliations
1 Departments of Mathematics and Computer Science, Ben-Gurion University, Beer Sheva-84105, Israel
2 Department of Mathematics, California State University, Los Angeles, CA-90032, United States
     

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Our main result is that the sequence (P(n) cos nα), n=1, 2, . . . , is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλn)∞n=0 is uniformly distributed modulo 1.
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  • Complete Uniform Distribution of Some Oscillating Sequences

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Authors

D. Berend
Departments of Mathematics and Computer Science, Ben-Gurion University, Beer Sheva-84105, Israel
G. Kolesnik
Department of Mathematics, California State University, Los Angeles, CA-90032, United States

Abstract


Our main result is that the sequence (P(n) cos nα), n=1, 2, . . . , is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλn)∞n=0 is uniformly distributed modulo 1.