Diophantine approximation by rational numbers of certain parity types (CONTRIBUTED TALK)
speaker: SeulBee Lee (Institute for Basic Science)abstract:
In the study of Diophantine approximation, a natural question is which rationals pq minimize
qx-p
with a bounded condition over q. We call such rationals the best approximations. The regular continued fraction provides an algorithm for generating the best approximations. From a broader perspective, we are interested in the best approximations with congruence conditions on their numerators and denominators. It is known that the continued fraction allowing only even integer partial quotients generates the best approximations whose numerator and denominator have differentparity. In this talk, we will reconstruct the even continued fraction map using a symbolic sequence of real numbers associated with a specific triangle group in the upper half-plane. Subsequently, we will define interval maps that yield algorithms for generating best approximations with other parity conditions. This is joint work with Dong Han Kim and Lingmin Liao.
timetable:
Thu 23 May, 15:00 - 15:30, Aula Dini
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