feat: port NumberTheory.ModularForms.JacobiTheta.Manifold (#5670)

Mathlib.lean

@@ -2405,6 +2405,7 @@ import Mathlib.NumberTheory.LucasPrimality
 import Mathlib.NumberTheory.Modular
 import Mathlib.NumberTheory.ModularForms.CongruenceSubgroups
 import Mathlib.NumberTheory.ModularForms.JacobiTheta.Basic
+import Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold
 import Mathlib.NumberTheory.ModularForms.SlashActions
 import Mathlib.NumberTheory.ModularForms.SlashInvariantForms
 import Mathlib.NumberTheory.Multiplicity

Mathlib/NumberTheory/ModularForms/JacobiTheta/Manifold.lean

@@ -0,0 +1,30 @@
+/-
+Copyright (c) 2023 David Loeffler. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: David Loeffler
+
+! This file was ported from Lean 3 source module number_theory.modular_forms.jacobi_theta.manifold
+! leanprover-community/mathlib commit 57f9349f2fe19d2de7207e99b0341808d977cdcf
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
+-/
+import Mathlib.NumberTheory.ModularForms.JacobiTheta.Basic
+import Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
+
+/-!
+# Manifold differentiability of the Jacobi theta function
+
+In this file we reformulate differentiability of the Jacobi theta function in terms of manifold
+differentiability.
+
+## TODO
+
+Prove smoothness (in terms of `Smooth`).
+-/
+
+
+open scoped UpperHalfPlane Manifold
+
+theorem mdifferentiable_jacobiTheta : MDifferentiable 𝓘(ℂ) 𝓘(ℂ) (jacobiTheta ∘ (↑) : ℍ → ℂ) :=
+  fun τ => (differentiableAt_jacobiTheta τ.2).mdifferentiableAt.comp τ τ.mdifferentiable_coe
+#align mdifferentiable_jacobi_theta mdifferentiable_jacobiTheta