Liouville Random functions and normal sets

Details Liouville Random functions and normal sets Liouville Random functions and normal sets

2005-09-14

arxiv.org/abs/math/0509315v1

Mathematics

Number Theory

6 pages, to appear in Acta Arithmetica

Scientific paper

We define a random Liouville function (\lambda_Q) which depends on a random set (Q) of primes and prove that (A_Q = \{n \in \mathbb{N} | \lambda_Q(n) = -1 \}) is normal almost everywhere. This fact enables us to generate a family of normal sets such that the equation (xy =z) is not solvable inside them. Additionally we prove that equations (xy=z^2, x^2 + y^2 = square, x^2 - y^2 = square) are solvable in any normal set and for any equation (xy=cn^2) ((c > 1 ), is not a square) there exists a normal set (A_c) such that the equation is not solvable inside (A_c).

Affiliated with

Also associated with

No associations

Rating

Liouville Random functions and normal sets 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 Liouville Random functions and normal sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Liouville Random functions and normal sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-680525