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SUMMARY:Yuta Suzuki (Nagoya University)
DTSTART:20201027T080000Z
DTEND:20201027T083000Z
DTSTAMP:20260423T010810Z
UID:JENTE/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/5/">On
  the irrationality of sums of reciprocals of Fibonacci numbers restricted 
 to prime-like indices</a>\nby Yuta Suzuki (Nagoya University) as part of J
 apan Europe Number Theory Exchange Seminar\n\n\nAbstract\nIn 1989\, André
 -Jeannin proved the irrationality of the sum of reciprocals of Fibonacci n
 umbers. A possible further question is to ask which subsums of reciprocal 
 of Fibonacci numbers are still irrational. In this talk\, we prove the irr
 ationality of such subsums with indices restricted to thin "prime-like" nu
 mbers. For example\, we can show the irrationality of the sum of reciproca
 ls of Fibonacci numbers of the prime-square indices. Our proof is an exten
 sion 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)\n
LOCATION:https://researchseminars.org/talk/JENTE/5/
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