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math.NT2020
Remarks about inhomogeneous pair correlations
Felipe A. Ramirez
Given an infinite subset , let denote its smallest elements. There is a rich and growing literature on the question of whether for typical $α…
math.NT2020
Dirichlet is not just Bad and Singular
Victor Beresnevich, Lifan Guan, Antoine Marnat +2
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions…
math.NT2020
A note on sequences not having metric Poissonian pair correlations
Felipe A. Ramirez
The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come…