Theorems · Theorem · number theory
quadraticChar_sum_zero
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F] [inst_2 : DecidableEq F],
ringChar F ≠ 2 → ∑ a, (quadraticChar F) a = 0The sum over the values of the quadratic character is zero when the characteristic is odd.
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- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeDecidableEq
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- MulCharstatement · cited by 186
- ringCharstatement and proof · cited by 73
- quadraticCharstatement · cited by 34
- MulChar.sum_eq_zero_of_ne_oneproof · cited by 9
- quadraticChar_ne_oneproof · cited by 1
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