On the irrationality of sums of reciprocals of Fibonacci numbers restricted to prime-like indices

Abstract: In 1989, André-Jeannin proved the irrationality of the sum of reciprocals of Fibonacci numbers. A possible further question is to ask which subsums of reciprocal of Fibonacci numbers are still irrational. In this talk, we prove the irrationality of such subsums with indices restricted to thin "prime-like" numbers. For example, we can show the irrationality of the sum of reciprocals of Fibonacci numbers of the prime-square indices. Our proof is an extension of Erdős's partial result (1968) towards the irrationality of $\sum_{p}\frac{1}{2^p-1}$. (joint work with D. Duverney and Y. Tachiya)

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October