Theorems · Theorem · number theory
gaussSum_eq_zero_of_isPrimitive_of_not_isPrimitive
∀ {N : ℕ} [inst : NeZero N] {R : Type u_1} [inst_1 : CommRing R] (e : AddChar (ZMod N) R) [IsDomain R]
{χ : DirichletCharacter R N}, χ.IsPrimitive → ¬e.IsPrimitive → gaussSum χ e = 0If χ is primitive, but e is not, then gaussSum χ e = 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsDomainstatement and proof · cited by 2,196
- ZModstatement and proof · cited by 1,024
- LT.lt.neproof · cited by 872
- LE.le.trans_ltproof · cited by 795
- AddCharstatement and proof · cited by 286
- DirichletCharacterstatement and proof · cited by 161
- gaussSumstatement and proof · cited by 29
- DirichletCharacter.conductorproof · cited by 29
- AddChar.mulShiftproof · cited by 26
- AddChar.IsPrimitivestatement and proof · cited by 22
- Nat.sInf_leproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- gaussSum_mulShift_of_isPrimitiveproof · cited by 1