Theorems · Theorem · number theory
UpperHalfPlane.norm_exp_two_pi_I_lt_one
∀ (τ : UpperHalfPlane), ‖Complex.exp (2 * ↑Real.pi * Complex.I * ↑τ)‖ < 1
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
Cited by7
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_sigma_mul_cexp_powproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- ModularForm.one_sub_eta_q_ne_zeroproof · cited by 2
- ModularForm.logDeriv_eta_eq_E2proof · cited by 1
- pi_mul_cot_pi_q_expproof · cited by 1
- iteratedDerivWithin_tsum_cexp_eqproof · cited by 1
- tsum_eisSummand_eq_tsum_sigma_mul_cexp_powproof · cited by 1