cuspFunction — Mathlib

English

The cuspFunction is defined as the periodic cusp function associated to f ∘ ofComplex, returning the analytic function F with F(z) = f(τ) when z = e^{2π i τ/n}. It encodes the q-expansion data of f.

Русский

CuspFunction задаётся как периодическая функция-куспт, связанная с f ∘ ofComplex; она кодирует q-разложение f.

LaTeX

$$$\text{cuspFunction} : \mathbb{C} \to \mathbb{C} \\ cuspFunction(z) = \text{Periodic.cuspFunction}(n, f \circ \mathrm{ofComplex})(z)$$$

Lean4

/-- The analytic function `F` such that `f τ = F (exp (2 * π * I * τ / n))`, extended by a choice of
limit at `0`.
-/
def cuspFunction : ℂ → ℂ :=
  Function.Periodic.cuspFunction n (f ∘ ofComplex)

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