## Seminar talk: “Sums of powers of binomials, their Apery limits, and Franel’s suspicions”

Date: 27/04/2022
Time: 14:00 - 15:00

Location: Hybrid (Zoom and RISC Seminarroom "Pond")

Ap\'ery'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 Ap\'ery limits and explore a particularly simple instance. We then explicitly determine the Ap\'ery 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. https://jku.zoom.us/j/94507814483?pwd=OTJRbEdhc1FlKzZZYklSQk9EaGZhdz09 Meeting-ID: 945 0781 4483 Password: HaveFun