Theorems · Theorem · number theory
norm_jacobiTheta_sub_one_le
∀ {τ : ℂ}, 0 < τ.im → ‖jacobiTheta τ - 1‖ ≤ 2 / (1 - Real.exp (-Real.pi * τ.im)) * Real.exp (-Real.pi * τ.im)An explicit upper bound for ‖jacobiTheta τ - 1‖.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites45
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 and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalproof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- le_of_ltproof · cited by 1,175
- tsumproof · cited by 1,148
- Real.expstatement and proof · cited by 871
Cited by1
Results whose statement or proof uses this declaration.
- isBigO_at_im_infty_jacobiTheta_sub_oneproof · cited by 0