The Atkin orthogonal polynomials for the Fricke groups of levels 5 and 7

作者：Sakai Yuichi^*

来源：International Journal of Number Theory, 2014, 10(8): 2243-2255.

DOI：10.1142/S1793042114500766

• Modular/quasimodular form
• Atkin%26apos
• s orthogonal polynomials

We define Atkin%26apos;s inner product for the Fricke groups of levels 5 and 7, and show that under certain condition the Atkin orthogonal polynomials in these cases exist. We also show the connection between extremal quasimodular forms of depth 1 and the Atkin orthogonal polynomials for these groups. Finally we propose a conjecture that relates our Atkin orthogonal polynomials to supersingular elliptic curves.

• 出版日期2014-12