Theorems · Theorem · number theory
tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow
∀ {k : ℕ},
3 ≤ k →
Even k →
∀ (z : UpperHalfPlane),
∑' (v : Fin 2 → ℤ), EisensteinSeries.eisSummand (↑k) v z =
2 * riemannZeta ↑k +
2 * ((-2 * ↑Real.pi * Complex.I) ^ k / ↑(k - 1).factorial) *
∑' (n : ℕ+), ↑((ArithmeticFunction.sigma (k - 1)) ↑n) * Complex.exp (2 * ↑Real.pi * Complex.I * ↑z) ^ ↑n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Complexstatement and proof · cited by 5,565
- Monoidproof · cited by 3,887
- mul_oneproof · cited by 3,885
- Equiv.symmproof · cited by 3,681
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.q_expansion_riemannZetaproof · cited by 1