Toward Khintchine's theorem with a moving target: extra divergence or finitely centered target

Gilbert Michaud, Felipe A. Ramírez

Sz{ü}sz's inhomogeneous version (1958) of Khintchine's theorem (1924) gives conditions on $\psi :\mathbb{N}\to {\mathbb{R}}_{\ge 0}$ under which for almost every real number $\alpha$ there ex…