Geodesic
Lacunarity of Dedekind η-products
Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 1-14

Voir la notice de l'article provenant de la source Cambridge University Press

The Dedekind η-function is defined bywhere τ lies in the upper half plane H = {tau;|Im(τ) > 0}, and x = e2πiτ. It is a modular form of weight 1⁄2 with a multiplier system. We define an η-product to be a function f (τ) of the formwhere rδ ε Z. This is a modular form of weight with a multiplier system. The Fourier coefficients of η-products are related to many well-known number-theoretic functions, including partition functions and quadratic form representation numbers. They also arise from representations of the “monster” group [3] and the Mathieu group M24 [13]. The multiplicative structure of these Fourier coefficients has been extensively studied. Recent papers include [1], [4], [5] and [6]. Here we study the connections between the density of the non-zero Fourier coefficients of f(τ) and the representability of f(τ) as a linear combination of Hecke character forms (defined in Section 4 below). We first make the following definition. 
Gordon, Basil; Robins, Sinai. Lacunarity of Dedekind η-products. Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 1-14. doi: 10.1017/S0017089500030329
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