Several irrationality problems for Ahmes series

Abstract: Proving (ir)rationality of infinite series of distinct unit fractions has been an active topic of research for decades, with numerous occasional breakthroughs. We will investigate what can be obtained using elementary techniques (such as iterative constructions and the probabilistic method) and address several problems posed by Paul Erdos throughout the 1980s. In particular, we will study one type of irrationality sequences introduced by Erdos and Graham, (almost entirely) resolve a question by Erdos on simultaneous rationality of two or more "consecutive" series, and give a negative answer to an "infinite-dimensional" conjecture by Stolarsky. This is joint work with Terence Tao (UCLA).

Mathematics

Audience: researchers in the topic

( paper | slides )

Comments: Online only. Link: www.theoryofnumbers.com/cant/

Combinatorial and additive number theory (CANT 2025)