Supercongruences modulo prime powers usually involve various combinatorial sequences and combinatorial identities. In this talk we give a survey of the speaker's various conjectures on supercongruences, one of which asserts that $(g_{pn}(-1)-g_n(-1))/(pn)3$ is a $p$-adic integer for any prime $p>5$ and positive integer $n$, where $$g_m(x):=\sum_{k=0}^m \binom{m}k2 \binom{2k}k x^k.$$
I will mention the motivations of those conjectural supercongruences as well as related known results.
Some conjectural supercongruences and related topics
27.06.2017 15:15 - 16:45
Organiser:
Ch. Krattenthaler
Location: