Holomorphicity of Eisenstein series #
We show that Eisenstein series of weight k
and level Γ(N)
with congruence condition
a : Fin 2 → ZMod N
are holomorphic on the upper half plane, which is stated as being
MDifferentiable.
Auxiliary lemma showing that for any k : ℤ
and (a : Fin 2 → ℤ)
the extension of eisSummand
is differentiable on {z : ℂ | 0 < z.im}
.