Theorems · Theorem · harmonic analysis
DirichletCharacter.fourierTransform_eq_gaussSum_mulShift
∀ {N : ℕ} [inst : NeZero N] (χ : DirichletCharacter ℂ N) (k : ZMod N),
ZMod.dft (⇑χ) k = gaussSum χ (ZMod.stdAddChar.mulShift (-k))- Defined in
- Mathlib.Analysis.Fourier.ZMod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Finsetproof · cited by 13,712
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- Complexstatement and proof · cited by 5,565
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- LinearEquivstatement · cited by 3,317
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- ZModstatement and proof · cited by 1,024
- neg_mulproof · cited by 654
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSumproof · cited by 1