Some special functions and their special values
Some special functions and their special values

Ken Ono, Emory University
Fine Hall 314
In his last letter to G. H. Hardy, Ramanujan wrote about his socalled "mock theta functions". These functions are now largely understood (by work of Zwegers) in the context of nonholomorphic Jacobi forms. Here we discuss recent work which pertains to the roles of these mock theta functions in Zagier's theory of quantum modular forms, and we construct new mock theta functions (one for each rational elliptic curve) from the Weierstrass zetafunction and we explain their relevance in the study of the arithmetic of elliptic curves.