On the Central Limit Theorem for Non-Archimedean Diophantine Approximations
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Abstract.We consider a Diophantine inequality:
on the set of formal Laurent series of negative degree. We show that under these two conditions: (i) qnΨ(n) is a monotone non-increasing and (ii) ∑nqnΨ(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.
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