An Improvement To Zaremba’s Conjecture

We introduce Zaremba’s Conjecture, with recent progress and application. Specifically, we will go over Bourgain and Kontorovich’s effective density one theorem, Local obstruction, and Frolenkov and Kan’s positive density theorem. Finally, we discuss how to combine the major arcs analysis and the minor arcs analysis in both papers to obtain a refined effective density one statement.