Affiliation: University of Wisconsin
Email: getz@math.wisc.edu
Title Of Talk: Systems of orthogonal polynomials arising from the modular j-function (joint work with S. Basha, H. Nover, and E. Smith)
Abstract: Let S_p(x) \in F_p[x] be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over F_p. Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier, we define an inner product <,>_{psi} for every psi(x) \in Q[x]. Suppose a system of orthogonal polynomials {P_{n,psi}(x)}_{n=0}^{infty} with respect to <,>_{psi} exists. We prove that if n is sufficiently large and psi(x) P_{n,psi}(x) is p-integral, then S_p(x) | psi(x) P_{n,psi} over F_p[x]. Further, we obtain an interpretation of these orthogonal polynomials as a p-adic limit of polynomials associated to p-adic modular forms.
Last update made Thu Nov 11 14:46:26 EST 2004.
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