Abstract: 

Borel and Dwork gave conditions on when a nice power series with rational number coefficients comes from a rational function in terms of meromorphic convergence radii at all places. Such a criterion was used in Dwork’s proof of the rationality of zeta functions of varieties over finite fields. Later, the work of André, Bost, Charles and many others generalized the rationality criterion of Dwork and deduced many applications in the arithmetic of differential equations and elliptic curves. In this talk, we will discuss some further refinements and generalizations of the criteria of André, Bost, and Charles and their applications to modular forms and irrationality of certain periods. This is joint work with Frank Calegari and Vesselin Dimitrov.

Time:

13:30-15:00, August 19.