On the arithmetic nature of coefficients of multiplicative eta-functions

In the article we study the arithmetic nature of the coefficients of multiplicative eta-products, also called McKay functions. For some functions it is possible to establish Hecke correspondence between the coefficients of McKay and Hecke grossen-characters of imaginary quadratic fields. For other McKay functions such a correspondence is impossible but their coefficients can be represented as sums containing Hecke characters. The emerging Hecke characters are written out explicitly. In the article we write the first ten coefficients for all McKay functions. Calculations are based on Euler's pentagonal formula. The article also talks about the connection between the coefficients of these functions and Shimura sums.