Math @ Duke

Publications [#292896] of Jayce R. Getz
Papers Published
 Basha, S; Getz, J; Nover, H; Smith, E, Systems of orthogonal polynomials arising from the modular jfunction,
Journal of Mathematical Analysis and Applications, vol. 289 no. 1
(2004),
pp. 336354, ISSN 0022247X [doi]
(last updated on 2018/03/21)
Abstract: Let Gfraktur signp(x) ε double struck F sign p[x] be the polynomial whose zeros are the jinvariants of supersingular elliptic curves over double struck F signp. Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier (Computational Perspectives on Number Theory (Chicago, IL, 1995), AMS/IP 7 (1998) 97126), we define an inner product 〈 , 〉ψ on ℝ[x] for every ψ(x) ε ℚ[x]. Suppose a system of orthogonal polynomials {Pn,ψ(x)}n=0∞ with respect to 〈, 〉ψ exists. We prove that if n is sufficiently large and ψ(x)Pn,ψ(x) is pintegral, then Gfraktur signp(x)\ψ(x)Pn(x) over double struck F signp[x]. Further, we obtain an interpretation of these orthogonal polynomials as a padic limit of polynomials associated to padic modular forms. © 2003 Elsevier Inc. All rights reserved.


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