The zeta-regularized product of odious numbers
Number Theory
2021-03-23 v2
Abstract
What is the product of all {\em odious} integers, i.e., of all integers whose binary expansion contains an odd number of 's? Or more precisely, how to define a product of these integers which is not infinite, but still has a "reasonable" definition? We will answer this question by proving that this product is equal to , where and are respectively the Euler-Mascheroni and the Flajolet-Martin constants.
Keywords
Cite
@article{arxiv.1906.10532,
title = {The zeta-regularized product of odious numbers},
author = {J. -P. Allouche},
journal= {arXiv preprint arXiv:1906.10532},
year = {2021}
}