# Prof. Dr. Armin Straub

Visit Date: 19/04/2022 - 29/04/2022

Home Institution: University of South Alabama

## Talks

27/04/202214:00 - 15:00Hybrid (Zoom and RISC Seminarroom "Pond")

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

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 ...

25/04/202213:30 - 14:30online via Zoom https://jku.zoom.us/j/94919458950?pwd=V2FMU2l3b2JFMmtCamgzMXlhNkRYQT09 Meeting-ID: 949 1945 8950 Password: 135891

### RISC Colloquium Talk: “Lucas congruences and congruence schemes”

It is a well-known and beautiful classical result of Lucas that, modulo a prime $p$, the binomial coefficients satisfy the congruences \begin{equation*} \binom{n}{k} \equiv \binom{n_0}{k_0} \binom{n_1}{k_1} \cdots \binom{n_r}{k_r}, \end{equation*} where $n_i$, respectively $k_i$, are the $p$-adic digits of $n$ and ...