summable_eta_q — Mathlib

English

CuspOrbits 𝒢 is the orbit-rel quotient of the action of 𝒢 on its cusps.

Русский

CuspOrbits 𝒢 — орбитный фактор отношения действия 𝒢 на cusp-ах.

LaTeX

$$$\\mathrm{CuspOrbits}(\\mathcal{G}) = \\mathrm{MulAction.orbitRel.Quotient}(\\mathcal{G}, \\mathrm{cusps\\_subMulAction}(\\mathcal{G}))$$$

Lean4

theorem summable_eta_q (z : ℍ) : Summable fun n ↦ ‖-eta_q n z‖ := by
  simp [eta_q, eta_q_eq_pow, summable_nat_add_iff 1, norm_exp_two_pi_I_lt_one z]

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