GENERALIZATION OF ATKIN'S ORTHOGONAL POLYNOMIALS AND SUPERSINGULAR ELLIPTIC CURVES.

In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod p for a prime p, one gets the locus of supersingular elliptic curves. Here we generalize this phenomenon by considering the continued fraction expansions of modular and quasimodular forms. [ABSTRACT FROM AUTHOR]