Mathlib Map

Theorems · Definition · number theory

UpperHalfPlane.im

UpperHalfPlane → ℝ

Imaginary part

Defined in
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
Cited by
128 results in Mathlib
Foundations
Depth 2 from the axioms, rests on 6 definitions · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UpperHalfPlane.im_pos · cited by 62UpperHalfPlane.im_posUpperHalfPlane.atImInfty · cited by 35UpperHalfPlane.atImInftyUpperHalfPlane.center · cited by 20UpperHalfPlane.centerUpperHalfPlane.im_ne_zero · cited by 18UpperHalfPlane.im_ne_zeroUpperHalfPlane.petersson · cited by 16UpperHalfPlane.peterssonUpperHalfPlane.verticalStrip · cited by 11UpperHalfPlane.verticalSt…EisensteinSeries.r · cited by 10EisensteinSeries.rUpperHalfPlane.coe_im · cited by 7UpperHalfPlane.coe_imUpperHalfPlane.im_inv_neg_coe_pos · cited by 7UpperHalfPlane.im_inv_neg…UpperHalfPlane.norm_exp_two_pi_I_lt_one · cited by 7UpperHalfPlane.norm_exp_t…ModularGroup.im_smul_eq_div_normSq · cited by 6ModularGroup.im_smul_eq_d…UpperHalfPlane.sinh_half_dist · cited by 6UpperHalfPlane.sinh_half_…EisensteinSeries.r1 · cited by 6EisensteinSeries.r1UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center · cited by 5UpperHalfPlane.cmp_dist_e…UpperHalfPlane.norm_qParam_lt_one · cited by 5UpperHalfPlane.norm_qPara…Real · cited by 25697RealUpperHalfPlane · cited by 626UpperHalfPlaneComplex.im · cited by 591Complex.imUpperHalfPlane.coe · cited by 288UpperHalfPlane.coeUpperHalfPlane.imCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by136

Results whose statement or proof uses this declaration.