OAI/NumberTheory/DukePrimeDegree/Arithmetic/CyclicRealCharacters.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

Real characters at a simple real zero

The actual Frobenius ideal character commutes with complex conjugation. Uniqueness of the entire nonprincipal Hecke continuation therefore makes the cyclic zero orders conjugation invariant. At a simple real zero the unique contributing character is real-valued.

  1. theorem OAI.DukePrimeDegree.conjugateLinearCharacter_conjugate line 24
  2. theorem OAI.DukePrimeDegree.conjugateLinearCharacter_one line 30
  3. theorem OAI.DukePrimeDegree.conjugateLinearCharacter_ne_one line 35
  4. theorem OAI.DukePrimeDegree.conjugate_artin_idealHom line 44
  5. theorem OAI.DukePrimeDegree.nonprincipalContinued_eq_of_idealHom line 62
  6. theorem OAI.DukePrimeDegree.cyclicHeckeFactor_order_conjugation line 78
  7. theorem OAI.DukePrimeDegree.real_character_of_simple_cyclic_zero line 101