 Congruence-class Eisenstein series

ID: congruence-class-eisenstein-series

For

k > 2

and

(x, y) \in (Z / N Z)^{2}

G_{k}^{(x, y)} (τ) = \sum_{( c , d ) \equiv ( x , y ) mod N ( c , d ) \neq = ( 0 , 0 )} (c τ + d)^{- k}

k

Γ (N)

(x, y)

γ \in S L_{2} (Z)

describes its slash transformation.

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