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Theorems · Definition · number theory

Subgroup.strictPeriods

{R : Type u_1} → [inst : Ring R] → Subgroup (GL (Fin 2) R) → AddSubgroup R

For a subgroup 𝒢 of GL(2, R), this is the additive group of x : R such that [1, x; 0, 1] ∈ 𝒢.

Defined in
Mathlib.NumberTheory.ModularForms.Cusps
Cited by
63 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Ring

Around this declaration

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

Subgroup.strictWidthInfty · cited by 19Subgroup.strictWidthInftyModularFormClass.analyticAt_cuspFunction_zero · cited by 14ModularFormClass.analytic…SlashInvariantFormClass.periodic_comp_ofComplex · cited by 11SlashInvariantFormClass.p…Subgroup.periods · cited by 10Subgroup.periodsone_mem_strictPeriods_SL · cited by 8one_mem_strictPeriods_SLSubgroup.isCusp_of_mem_strictPeriods · cited by 6Subgroup.isCusp_of_mem_st…Subgroup.strictWidthInfty_mem_strictPeriods · cited by 5Subgroup.strictWidthInfty…Subgroup.strictWidthInfty_pos_iff · cited by 5Subgroup.strictWidthInfty…Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem · cited by 4Subgroup.strictPeriods_eq…Subgroup.strictPeriods_eq_zmultiples_strictWidthInfty · cited by 4Subgroup.strictPeriods_eq…ModularForm.qExpansion_mul · cited by 4ModularForm.qExpansion_mulModularForm.qExpansion_smul · cited by 4ModularForm.qExpansion_sm…Subgroup.strictPeriods_SL2Z · cited by 3Subgroup.strictPeriods_SL…Subgroup.strictPeriods_le_periods · cited by 3Subgroup.strictPeriods_le…Subgroup.strictWidthInfty_eq_one_of_T_mem · cited by 3Subgroup.strictWidthInfty…DFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingMatrix · cited by 4303MatrixSubgroup · cited by 3593SubgroupAddSubgroup · cited by 3232AddSubgroupMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupAddSubgroup.comap · cited by 123AddSubgroup.comapSubgroup.toAddSubgroup · cited by 20Subgroup.toAddSubgroupMatrix.GeneralLinearGroup.upperRightHom · cited by 14GeneralLinearGroup.upperR…AddChar.toAddMonoidHom · cited by 5AddChar.toAddMonoidHomSubgroup.strictPeriodsCITED BYCITES

Cites10

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

Cited by68

Results whose statement or proof uses this declaration.