feat(Wikipedia): add ERH for Dedekind zeta

FormalConjectures/Wikipedia/ExtendedRiemannHypothesis.lean

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+/-
+Copyright 2025 The Formal Conjectures Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    https://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+-/
+
+import FormalConjectures.Util.ProblemImports
+
+/-!
+# Extended Riemann Hypothesis (Dedekind zeta functions)
+
+*Reference:* [Wikipedia](https://en.wikipedia.org/wiki/Generalized_Riemann_hypothesis)
+-/
+
+namespace ExtendedRiemannHypothesis
+
+/-- The (open) critical strip $\{ s \in \mathbb{C} \mid 0 < \Re(s) < 1 \}$. -/
+def IsInCriticalStrip (s : ℂ) : Prop :=
+  0 < s.re ∧ s.re < 1
+
+/--
+The **Extended Riemann Hypothesis** (ERH) for Dedekind zeta functions asserts that if
+$K$ is a number field and $\zeta_K(s)$ is its Dedekind zeta function, then every zero of
+$\zeta_K(s)$ in the critical strip satisfies $\Re(s) = \tfrac12$.
+-/
+@[category research open, AMS 11 12 30]
+theorem extended_riemann_hypothesis_dedekindZeta (K : Type*) [Field K] [NumberField K] (s : ℂ)
+    (hs_strip : IsInCriticalStrip s) (hs : NumberField.dedekindZeta K s = 0) :
+    s.re = 1 / 2 := by
+  sorry
+
+end ExtendedRiemannHypothesis