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SUPERSINGULAR RANK TWO DRINFEL'D MODULES AND ANALOGS OF ATKIN'S ORTHOGONAL POLYNOMIALS

DORIS DOBI

Department of Mathematics, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012-1185, USA

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NICHOLAS WAGE

Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, 02138-3758, USA

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, and

IRENA WANG

Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA

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https://doi.org/10.1142/S1793042109002444Cited by:2 (Source: Crossref)

Abstract

The theory of elliptic curves and modular forms provides a precise relationship between the supersingular j-invariants and the congruences between modular forms. Kaneko and Zagier discuss a surprising generalization of these results in their paper on Atkin orthogonal polynomials. In this paper, we define an analog of the Atkin orthogonal polynomials for rank two Drinfel'd modules.

Keywords:

AMSC: 11F52

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