Takagi Function Identities on Dyadic Rationals

Abstract

The number of unbalanced interior nodes of divide-and-conquer trees on $n$ leaves is known to form a sequence of dilations of the Takagi function on dyadic rationals. We use this fact to derive identities on the Takagi function and on the Hamming weight of an integer in terms of the Takagi function.

arXiv comment11 pages, 1 figure. This paper is a small portion of arXiv:2108.11496 with some additions, split for publication. Version 2 adds references to another proof of the weight theorem and makes some notation changes. Version 3 is the published version