The 26th power of Dedekind's ?-function

• Autores: Heng Huat Chan, Shaun Cooper, Pee Choon Toh
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 532-543
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.12.003
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• Resumen

  • 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