Title

On The Atkin Polynomials

Keywords

Associated Jacobi polynomials; Asymptotics; Birth and death process polynomials; Hecke operators; Modular function; Scaled invariant; Supersingular polynomials; Weight functions

Abstract

We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identification then takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that corecursive polynomials may lead to interesting sets of orthogonal polynomials.

Publication Date

1-1-2014

Publication Title

Pacific Journal of Mathematics

Volume

272

Issue

1

Number of Pages

111-130

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.2140/pjm.2014.272.111

Socpus ID

84911212248 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84911212248

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