자렘바의 추측

메모

Zaremba's conjecture (1971) states that every positive integer number d can be represented as a denominator of a finite continued fraction \(b/d = [d_1,d_2,...,d_k]\), with all partial quotients \(d_1,d_2,\cdots,d_k\) being bounded by an absolute constant \(A\).

관련논문

• Kan, I. D. ‘A Strengthening of a Theorem of Bourgain-Kontorovich-IV’. arXiv:1503.06132 [math], 20 March 2015. http://arxiv.org/abs/1503.06132.
• Bourgain, Jean, and Alex Kontorovich. ‘On Zaremba’s Conjecture’. Annals of Mathematics 180, no. 1 (1 July 2014): 137–96. doi:10.4007/annals.2014.180.1.3. http://arxiv.org/abs/1103.0422.