《数论与代数几何》讨论班

题目：Regularity in partial quotients of some algebraic continued fractions over finite fields

报告人：姚家燕教授（清华大学）

摘要：

For a given algebraic formal power series with coefficients in a finite field, what kind of regularity (if any) can be expected for its partial quotients in continued fraction expansion? Such a question is natural, since by the famous CKMFR's theorem, the coefficients of an algebraic power series over a finite field form an automatic sequence. Certain algebraic continued fractions are such that the sequence of the leading coefficients of the partial quotients is automatic. Here we give some rather general families of such sequences. Moreover, inspired by these examples, we give several criteria on automatic sequences, which allow us to obtain new families of automatic sequences in an arbitrary finite field.

时间：4月20日（周五）下午4:30-5:30

地点：首师大新教二楼827教室

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