Rational approximation with chosen numerators
arXiv:2502.08335
Abstract
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, both probabilistic and deterministic, draw connections to twisted diophantine approximation, and present a simple application, related to possible correlations between trace functions and dynamical sequences.
27 pages; to appear in IMRN; changed minor typographical mistakes and added some remarks