Modular partition vectors over an interval

Abstract

Modular partition vector is a generalization of the length of continued fraction to a nontrivial congruence subgroup. It was shown that its distribution over the unit interval is asymptotically Gaussian. In the talk, I will discuss the distribution over a sub-interval. A main ingredient is the introduction of an interval operator that is a variant of a weighted transfer operator on the space of continuously differentiable functions on the unit interval. I will discuss one consequence towards a classical problem, namely the distribution of modular inverses. This is joint work with Jungwon Lee.