zeta — Mathlib

English

Define the Dirichlet zeta function on natural numbers by ζ(0) = 0 and ζ(n) = 1 for n > 0.

Русский

Определим функцию дзета Дирихле на натуральных числах: ζ(0) = 0 и ζ(n) = 1 при n > 0.

LaTeX

$$def zeta : ArithmeticFunction ℕ := ⟨fun x => ite (x = 0) 0 1, rfl⟩$$

Lean4

/-- `ζ 0 = 0`, otherwise `ζ x = 1`. The Dirichlet Series is the Riemann `ζ`. -/
def zeta : ArithmeticFunction ℕ :=
  ⟨fun x => ite (x = 0) 0 1, rfl⟩

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