English
The sum over the divisors antidiagonal with geometric weights is summable under |r|<1.
Русский
Сумма по антидиагонали делителей с геометрическими весами суммируема при |r|<1.
LaTeX
$$$$ \text{Summable} \; \text{divisorsAntidiagonalAux} \text{(r, k)} $$$$
Lean4
/-- The `vonMangoldt` function is the function on natural numbers that returns `log p` if the input can
be expressed as `p^k` for a prime `p`.
In the case when `n` is a prime power, `Nat.minFac` will give the appropriate prime, as it is the
smallest prime factor.
In the `ArithmeticFunction` locale, we have the notation `Λ` for this function.
This is also available in the `ArithmeticFunction.vonMangoldt` locale, allowing for selective
access to the notation.
-/
noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
