ArithmeticFunction — Mathlib

English

A natural-to-arithmetic-coercion is defined by sending each natural input to its image in R via the natural embedding.

Русский

Сущности: перенос натуральных значений в аритметическую функцию над R через естественное вложение.

LaTeX

$$$\\text{natToArithmeticFunction}: (\\mathbb{N} \\to \\mathbb{N}) \\to (\\mathbb{N} \\to R): (f)(n) = \\uparrow f(n)$$$

Lean4

/-- An arithmetic function is a function from `ℕ` that maps 0 to 0. In the literature, they are
  often instead defined as functions from `ℕ+`. Multiplication on `ArithmeticFunctions` is by
  Dirichlet convolution. -/
def ArithmeticFunction [Zero R] :=
  ZeroHom ℕ R

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