Counting Points over finite fields and hypergeometric functions


Youngae Lee

09:30:00 - 11:30:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we discuss a result that the number of points over a finite field on the Legendre family of elliptic curves can be written in terms of a hypergeometric function modulo p.
  Moreover, we consider the extension of this result, due to Igusa, to a family of monomial deformations of a diagonal hypersurface.
We also see explicit relationships between the number of points and generalized hypergeometric functions as well as their finite field analogues.
This talk is based on the paper : Salerno, Adriana Counting points over finite fields and hypergeometric functions. Funct. Approx. Comment. Math. 49 (2013), no. 1, 137–157