Resumen de The 26th power of Dedekind's ?-function

Heng Huat Chan, Shaun Cooper, Pee Choon Toh

• We prove a simple and explicit formula, which expresses the 26th power of Dedekind's ?-function as a double series. The proof relies on properties of Ramanujan's Eisenstein series P, Q and R, and parameters from the theory of elliptic functions.

  The formula reveals a number of properties of the product , for example its lacunarity, the action of the Hecke operator, and sufficient conditions for a coefficient to be zero.

  Keywords: 26th power; Dedekind eta function; Eisenstein series; Hecke operator; Lacunary; Macdonald identity; Ramanujan differential equations; Winquist's identity