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math.NT2025
Rational approximation with chosen numerators
Manuel Hauke, Emmanuel Kowalski
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results,…
math.NT2022
On the distribution of partial quotients of reduced fractions with fixed denominator
Christoph Aistleitner, Bence Borda, Manuel Hauke
In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions , where is fixed and runs throu…
math.NT2021
Weak Poissonian Correlations
Manuel Hauke, Agamemnon Zafeiropoulos
We examine a property of sequences called Poissonian pair correlations with parameter (abbreviated as -PPC). We prove that when the property of…