Theorems · Theorem · number theory
Complex.isIntegral_two_mul_sin_rat_mul_pi
∀ (q : ℚ), IsIntegral ℤ (2 * Complex.sin (↑q * ↑Real.pi))
2 sin(q * π) for q : ℚ is integral over ℤ, using the complex sin function.
- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.Iproof · cited by 866
- Complex.expproof · cited by 612
- IsIntegralstatement and proof · cited by 427
- Complex.sinstatement · cited by 258
- two_ne_zeroproof · cited by 251
- mul_div_cancel₀proof · cited by 77
- IsIntegral.mulproof · cited by 24
- IsIntegral.subproof · cited by 7
- Complex.isIntegral_exp_rat_mul_pi_mul_Iproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Complex.isAlgebraic_sin_rat_mul_piproof · cited by 1