  Hypergeometric functions over finite fields were introduced by Greene in the
1980s as a finite field analogue of classical hypergeometric series. These
functions, and their generalizations, naturally lend themselves to, and have
been widely used in, character sum evaluations and counting points on algebraic
varieties. More interestingly, perhaps, are their links to Fourier coefficients
of modular forms. In this paper, we outline the main results in this area and
also conjecture 13 new relations.
