Namespace UpperHalfPlane 28 theorems
- Uniqueness of q-expansions of periodic holomorphic functions
UpperHalfPlane.eq_of_forall_qCoeff_eq0 below · cited by 32 · depth 10 - q-expansion of f(dτ): coefficients shifted by d
UpperHalfPlane.qCoeff_comp_heckeDiagMatrix_smul0 below · cited by 57 · depth 10 - q-expansion coefficients of Uₚ f: aₙ(Uₚf)=aₙₚ(f)
UpperHalfPlane.qCoeff_heckeU0 below · cited by 18 · depth 10 - q-expansion coefficients of Tₚ f
UpperHalfPlane.qCoeff_heckeT0 below · cited by 5 · depth 11 - Width rescaling of q-expansions: q_h = q_{Mh}^M
UpperHalfPlane.qExpansion_coeff_nat_mul0 below · cited by 2 · depth 12 - Stabiliser order divides twice the meromorphic order at τ
UpperHalfPlane.natCard_stabilizer_dvd_two_mul_of_meromorphicOrderAt_eq0 below · cited by 4 · depth 13 - q-expansion of a finite product of functions on H
UpperHalfPlane.qExpansion_prod0 below · cited by 1 · depth 13 - Fibres of F near a non-cuspidal value stay in Γ U
UpperHalfPlane.eventually_forall_exists_smul_mem_of_meromorphicOrderAt_pos0 below · cited by 2 · depth 14 - Residues of f dτ/(F-t) on X(Γ)
UpperHalfPlane.exists_residue_cuspForm_div_sub8 below · cited by 2 · depth 14 - Periodic primitives of bounded periodic holomorphic functions on H
UpperHalfPlane.isBoundedAtImInfty_of_hasDerivAt_of_periodic0 below · cited by 1 · depth 14 - Vanishing of stabiliser-weighted residue sums for weight-2 invariants
UpperHalfPlane.sum_residue_div_card_stabilizer_eq_zero_of_slashInvariant7 below · cited by 5 · depth 14 - Periodicity of a primitive of a periodic form vanishing at i∞
UpperHalfPlane.apply_add_eq_apply_of_hasDerivAt_of_isZeroAtImInfty0 below · cited by 1 · depth 15 - Residue theorem on X(1): weighted residues sum to zero
UpperHalfPlane.levelOne_sum_residue_div_card_stabilizer_eq_zero6 below · cited by 1 · depth 15 - Vanishing of a folded strip integral against a cut-off
UpperHalfPlane.integral_mul_eq_zero_of_periodic_of_tendsto_atImInfty1 below · cited by 1 · depth 16 - Linear independence over K descends from q-expansion coefficients to ℂ
UpperHalfPlane.linearIndependent_complex_of_qExpansion_coeff_mem0 below · cited by 3 · depth 16 - Vanishing constant Fourier coefficient of a function decaying at i∞
UpperHalfPlane.intervalIntegral_eq_zero_of_periodic_of_tendsto_atImInfty0 below · cited by 2 · depth 17 - Exponential decay at i∞ kills low q-expansion coefficients
UpperHalfPlane.qExpansion_coeff_eq_zero_of_isBigO_exp_neg0 below · cited by 1 · depth 17 - Change of width in a q-expansion
UpperHalfPlane.qExpansion_coeff_mul_width0 below · cited by 6 · depth 17 - q-expansion coefficients of the sum of h₀ integer translates
UpperHalfPlane.qExpansion_coeff_sum_vAdd_eq_mul_coeff0 below · cited by 1 · depth 17 - Fricke conjugate of U_q as a sum over lower-unipotent cosets
UpperHalfPlane.sum_slash_S_mul_T_zpow_mul_S_inv_apply_eq_of_fricke_heckeU0 below · cited by 2 · depth 22 - Fixing τ₀ acts by a multiplier in the Cayley coordinate
UpperHalfPlane.cayley_smul_eq_mul_cayley0 below · cited by 1 · depth 23 - A smooth dipole on H with divisor s-b
UpperHalfPlane.exists_localModel_pair_integral_mul_dbarLogDeriv_eq3 below · cited by 2 · depth 23 - Periodicity of F∘σ when σ T^hσ⁻¹∈Γ
UpperHalfPlane.periodic_comp_smul_of_conj_T_pow_mem0 below · cited by 1 · depth 23 - Orbits of a discrete determinant-one subgroup of GL₂(ℝ) are discrete
UpperHalfPlane.eventually_nhdsNE_not_exists_smul_eq_of_discreteTopology_of_det_eq_one0 below · cited by 2 · depth 28 - Point stabilisers in discrete determinant-one subgroups are finite cyclic
UpperHalfPlane.finite_stabilizer_and_isCyclic_of_det_eq_one0 below · cited by 5 · depth 28 - Even order of stabilisers when -1 ∈ Γ
UpperHalfPlane.two_dvd_natCard_stabilizer_of_neg_one_mem1 below · cited by 4 · depth 28 - Automorphy factor at a fixed point in H
UpperHalfPlane.denom_eq_of_smul_eq_self0 below · cited by 1 · depth 29 - Stabiliser order divides twice the meromorphic order at τ
UpperHalfPlane.natCard_stabilizer_dvd_two_mul_of_meromorphicOrderAt_eq_of_det_eq_one0 below · cited by 2 · depth 29