Non-convex geometry of numbers and continued fractions

2021/04/16 by Nickolas Andersen, Andersen, Nickolas, William Duke +5
Mathematics · #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2104.08385

Abstract

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≥ 1. We extend this construction to the region 0

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