Theorems · Theorem · number theory
norm_exp_mul_sq_le
∀ {τ : ℂ},
0 < τ.im → ∀ (n : ℤ), ‖Complex.exp (↑Real.pi * Complex.I * ↑n ^ 2 * τ)‖ ≤ Real.exp (-Real.pi * τ.im) ^ n.natAbs- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.reproof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.Istatement and proof · cited by 866
- Complex.expstatement · cited by 612
- Complex.imstatement and proof · cited by 591
Cited by1
Results whose statement or proof uses this declaration.
- norm_jacobiTheta_sub_one_leproof · cited by 1