Special hypergeometric motives and ($p$-adic) $L$-functions

I will talk about reincarnation of an arithmetic phenomenon going back to Ramanujan's work from 1914,
in terms of hypergeometric motives--a notion introduced and studied recently by F. Rodriguez-Villegas,
D.Roberts, M.Watkins and others. The developed theory allows one to investigate, both rigorously and experimentally, several remarkable features including connections to modular forms, (expectedly) Siegel
modular forms and their $p$-adic $L$-functions.
This is joint work with Alexey Panchishkin.