Talk:Hecke operator

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Please may we have something on the action of Hecke operators on functions of weight zero? This action is given by the Faber polynomial. It generalizes the standard operator to all modular levels and is the basis for defining replicable functions of which a subset is monstrous moonshine.

John McKay130.54.16.82 (talk) 09:20, 2 May 2008 (UTC)Reply

Define a Hecke operator T_n that maps a lattice L < C to its sublattices of index n and induces an action on functions of the lattice L.

66.130.86.141 (talk) 18:51, 5 February 2010 (UTC) John McKayReply

Currently, I learn math from such resources as Wikipedia. I know that's not the correct way, but it's easier for me and I haven't started the correct way yet. It may be difficult for me to find the books to use. So, I'd like someone to help me by telling what book I should read to understand why it's ${\displaystyle \Gamma \backslash M_{m}}$. To me, it looks like it's the same as ${\displaystyle \Gamma }$, except empty for ${\displaystyle m=1}$, and ${\displaystyle M_{m}/\Gamma }$ would fit better Orisphera2 (talk) 10:01, 6 July 2024 (UTC)Reply

By ${\displaystyle M_{m}/\Gamma }$, I mean a generalisation of the quotient that I think would be natural (in the common sense), but I don't know how to call or denote it. It's the subfield of the quotient of the common superfield by the denominator obtained by choosing only the items corresponding to the ones from the numerator Orisphera2 (talk) 10:16, 6 July 2024 (UTC)Reply