OAI/NumberTheory/DukePrimeDegree/Arithmetic/ZetaIsomorphism.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Continued zeta orders respect field isomorphisms

The Dirichlet coefficients are preserved by a number-field isomorphism. Uniqueness of analytic continuation therefore preserves the zero order, including for the bottom field in a normal closure.

  1. lemma OAI.DukePrimeDegree.removedEulerPolynomial_one line 23
  2. theorem OAI.DukePrimeDegree.zetaZeroOrder_algEquiv line 33
  3. theorem OAI.DukePrimeDegree.zetaMultiplicity_algEquiv line 58
  4. theorem OAI.DukePrimeDegree.fixedFieldMultiplicity_top_eq line 66
  5. theorem OAI.DukePrimeDegree.zetaMultiplicity_eq_zero_of_completed_ne_zero line 76
  6. theorem OAI.DukePrimeDegree.rational_zetaMultiplicity_zero_scaled line 87