Special hypergeometric motives and their 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 Fernando Rodriguez-Villegas, 
David Roberts, Mark Watkins and others. The developed theory allows one 
to investigate, both rigorously and experimentally, several remarkable 
features including connections to modular forms, (expectedly) Hilbert 
and Siegel modular forms and their $L$-functions. The talk is joint work 
in progress with Lassina Dembélé, Alexey Panchishkin and John Voight.