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SUMMARY:Junnosuke Koizumi (RIKEN iTHEMS)
DTSTART:20260210T130000Z
DTEND:20260210T140000Z
DTSTAMP:20260423T021338Z
UID:OWNS/161
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/161/">I
 rrationality Sequences</a>\nby Junnosuke Koizumi (RIKEN iTHEMS) as part of
  One World Numeration seminar\n\n\nAbstract\nSometimes one can prove the i
 rrationality of the sum of reciprocals of a sequence of positive integers 
 using only information about the growth rate of the sequence. Erdős and S
 traus introduced the notion of an irrationality sequence in order to isola
 te nontrivial aspects of this relationship. Despite its elementary formula
 tion\, the theory of irrationality sequences still contains many open prob
 lems. For instance\, the question of whether $2^{2^n}$ is a (type 2) irrat
 ionality sequence is a particularly interesting open problem. Recently\, K
 ovač and Tao obtained several interesting results on the asymptotic behav
 ior of irrationality sequences. We study sums of reciprocals of doubly exp
 onential sequences and show\, among other results\, that there are at most
  countably many real numbers $a>1$ for which $a^{2^n}$ is a (type 2) irrat
 ionality sequence. We also explain how such questions are related to certa
 in greedy Egyptian fraction expansions.\n
LOCATION:https://researchseminars.org/talk/OWNS/161/
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