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On the fractional Parts of a^n/n

Author
Cilleruelo, J.; Luca, F.; Kumchev, A.; Rue, J.; Shparlinski, I.
Type of activity
Journal article
Journal
Bulletin of the London Mathematical Society
Date of publication
2013-09-30
Volume
45
Number
2
First page
249
Last page
256
DOI
https://doi.org/10.1112/blms/bds084 Open in new window
Repository
http://hdl.handle.net/2117/104257 Open in new window
Abstract
We give various results about the distribution of the sequence {a n/n}n=1 modulo 1, where a = 2 is a fixed integer. In particular, we find and infinite subsequence A such that {a n/n}n¿A is well distributed. Also we show that for any constant c > 0 and a sufficiently large N, the fractional parts of the first N terms of this sequence hit every interval J ¿ [0, 1] of length |J | = cN -0.47
Citation
Cilleruelo, J., Luca, F., Kumchev, A., Rue, J., Shparlinski, I. On the fractional Parts of a^n/n. "Bulletin of the London Mathematical Society", 30 Setembre 2013, vol. 45, núm. 2, p. 249-256.
Keywords
Theorems
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

  • Cilleruelo, Javier  (author)
  • Luca, Florian  (author)
  • Kumchev, Angel  (author)
  • Rue Perna, Juan José  (author)
  • Shparlinski, Igor  (author)

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