An Observation of Rankin on Hankel Determinants.

While studying the location of the zeros of the Eisenstein series Ek(z), Rankin considered the determinants ∆n of an associated Hankel matrix. He observed that the first few possess remarkable factorizations, and expressed the hope that a general theorem explaining these factorizations could be found. In this note we provide such a theorem by giving an explicit formula for ∆n using work of Kaneko and Zagier on Atkin polynomials.