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) ∑ n qnΨ(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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Mathematics Subject Classification (2000): 11J61, 11K60
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Deligero, E., Nakada, H. On the Central Limit Theorem for Non-Archimedean Diophantine Approximations. manuscripta math. 117, 51–64 (2005). https://doi.org/10.1007/s00229-005-0542-9
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DOI: https://doi.org/10.1007/s00229-005-0542-9