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Zaremba’s conjecture
Xin Zhang 张欣 (香港大学)
2026-08-28 (Fri) 15:00 — Room 102, SCMS
Abstract: Motivated by the construction of optimal sample sets for numerical integration, Zaremba (1971) proposed the following celebrated conjecture in number theory: there exists an absolute constant M > 0 such that every natural number q is the denominator of some reduced fraction a/q whose partial quotients are bounded by M. That is, the continued fraction expansion a/q = 1 / (a1 + 1 / (a2 + 1 / (… + 1 / an))) satisfies ai <= M for all 1 <= i <= n. In this talk, I will survey the history of Zaremba’s conjecture and outline the methods behind its recent resolution.
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