Non-convex geometry of numbers and continued fractions
Non-convex geometry of numbers and continued fractions
In recent work, the first two authors constructed a generalized continued fraction called the $p$-continued fraction, characterized by the property that its convergents (a subsequence of the regular convergents) are best approximations with respect to the $L^p$ norm, where $p\geq 1$.We extend this construction to the region $0<p<1$, where now …