Algorithmic Combinatorics Seminar
Title: Sums of powers of binomials, their Apery limits, and Franel's suspicions
Speaker: Prof. Armin Straub
(University of South Alabama, U.S.A.)
Time and Location: Wednesday, April 27, 2022, 2 p.m.
RISC pond seminar room and Zoom
Abstract: Apery's proof of the irrationality of zeta(3) relies on
representing that value as the limit of the quotient of two rational
solutions to a three-term recurrence. We review such Apery limits and
explore a particularly simple instance. We then explicitly determine the
Apery limits attached to sums of powers of binomial coefficients. As
an application, we prove a weak version of Franel's conjecture on the
order of the recurrences for these sequences. This is based on joint
work with Wadim Zudilin.