For a class of Picard-Fuchs equations, one can find special arguments with extra polynomial dependencies between solutions by using 'poor man's adeles', i.e., by gluing material modulo different primes using the Chinese remainder theorem.
Alin Bostan (INRIA Paris)
Francis Brown (U Oxford)
Herwig Hauser (U of Vienna)
Shihoko Ishii (U Tokyo)
Hiraku Kawanoue (Chubu U, Kasugai City)
Michael Singer (NC State U, Raleigh)