On the central limit theorem for non-archimedean diophantine approximations

We consider a Diophantine inequality: [InlineMediaObject not available: see fulltext.] on the set of formal Laurent series of negative degree. We show that under these two conditions: (i) q ⁿ Ψ(n) is a monotone non-increasing and (ii) ∑_n q ⁿ Ψ(n)=∞, a central limit theorem holds for the number of solutions. The proof is based on the construction of a non-stationary one dependent process associated with the Diophantine inequality.