# On Zaremba's Conjecture on Continued Fractions

## On Zaremba's Conjecture on Continued Fractions - Jean Bourgain

Jean Bourgain
Institute for Advanced Study
February 14, 2012
Zaremba's 1971 conjecture predicts that every integer appears as the denominator of a finite continued fraction whose partial quotients are bounded by an absolute constant. We confirm this conjecture for a set of density one.