There are infinitely many limit points of the fractional parts of powers

Details There are infinitely many limit points of the fractional parts of powers There are infinitely many limit points of the fractional parts of powers

2005-12-14

arxiv.org/abs/math/0512314v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 391-397

Mathematics

Number Theory

7 pages

Scientific paper

Suppose that $\al>1$ is an algebraic number and $\xi>0$ is a real number. We
prove that the sequence of fractional parts $\{\xi \al^n\},$ $n =1,2,3,...,$
has infinitely many limit points except when $\al$ is a PV-number and $\xi \in
\Q(\al).$ For $\xi=1$ and $\al$ being a rational non-integer number, this
result was proved by Vijayaraghavan.

Affiliated with

Also associated with

No associations

Rating

There are infinitely many limit points of the fractional parts of powers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with There are infinitely many limit points of the fractional parts of powers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and There are infinitely many limit points of the fractional parts of powers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-81815