The Duffin-Schaeffer type conjectures in various local fields

Abstract

This paper discovers a new phenomenon about the Duffin-Schaeffer conjecture, which claims that λ(∩ ∞ m=1 ∪ ∞ n=m E n ) = 1 if and only if n λ(E n ) = ∞, where λ denotes the Lebesgue measure on R/Z, 2000 Mathematics Subject Classification. 11J83.