NAME: Scott Ahlgren

 ADDRESS: Department of Mathematics
			Colgate University		
			Hamilton, NY 13346	
 EMAIL ADDRESS: sahlgren@mail.colgate.edu
 
 TITLE OF TALK: Gaussian hypergeometric series, elliptic curves, and
 combinatorial congruences.
  
 ABSTRACT OF TALK:   Gaussian hypergeometric series were first introduced
 by J. Greene as finite field analogues of classical hypergeometric series. 
 Recent works have shown that special values of these series are connected to 
 much of number theoretic and combinatorial interest.  In a recent paper, for
 example, Ken Ono and I uncover such connections involving
 modular forms, p-adic analysis, and the Wilf-Zeilberger identity
 proving method;   these connections yield a proof
 of one of Beukers' "supercongruence'' conjectures for the Apery numbers.
 In this talk I will discuss similar phenomena involving other
 families of Gaussian hypergeometric series and  the elliptic curves and  
 combinatorial congruences to which they are related. In particular, I will 
 show how these connections lead to a proof of another of Beukers' 
 supercongruence conjectures.

 
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