feat(NumberTheory/LSeries): introduce notations (#11253)

This just introduces `L` as a short notation for `LSeries` and `↗f` as notation for `fun n : ℕ ↦ (f n : ℂ)`,
both scoped to `LSeries.notation`. The latter makes it convenient to use arithmetic functions
or Dirichlet characters (or anything that coerces to a function `N → R`, where `ℕ` coerces
to `N` and `R` coerces to `ℂ`) as arguments to `LSeries` etc. The first is for convenience (and agreement with informal math, where we write "L(f, s)"), and the second one considerably simplifies statements involving Dirichlet characters or arithmetic functions like the von Mangoldt function and their L-series.

See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.

Mathlib/NumberTheory/LSeries/Basic.lean

@@ -36,6 +36,13 @@ Given a sequence `f: ℕ → ℂ`, we define the corresponding L-series.
  * `LSeriesSummable.isBigO_rpow`: if the `LSeries` of `f` is summable at `s`,
     then `f = O(n^(re s))`.
 
+## Notation
+
+We introduce `L` as notation for `LSeries` and `↗f` as notation for `fun n : ℕ ↦ (f n : ℂ)`,
+both scoped to `LSeries.notation`. The latter makes it convenient to use arithmetic functions
+or Dirichlet characters (or anything that coerces to a function `N → R`, where `ℕ` coerces
+to `N` and `R` coerces to `ℂ`) as arguments to `LSeries` etc.
+
 ## Tags
 
 L-series
@@ -48,7 +55,6 @@ L-series
 * Move `LSeries_add` and friends to a new file on algebraic operations on L-series
 -/
 
-
 open scoped BigOperators
 
 open Complex
@@ -186,6 +192,21 @@ theorem LSeriesSummable_iff_of_re_eq_re {f : ℕ → ℂ} {s s' : ℂ} (h : s.re
 #align nat.arithmetic_function.l_series_summable_iff_of_re_eq_re LSeriesSummable_iff_of_re_eq_re
 
 
+/-!
+### Notation
+-/
+
+@[inherit_doc]
+scoped[LSeries.notation] notation "L" => LSeries
+
+/-- We introduce notation `↗f` for `f` interpreted as a function `ℕ → ℂ`.
+
+Let `R` be a ring with a coercion to `ℂ`. Then we can write `↗χ` when `χ : DirichletCharacter R`
+or `↗f` when `f : ArithmeticFunction R` or simply `f : N → R` with a coercion from `ℕ` to `N`
+as an argument to `LSeries`, `LSeriesHasSum`, `LSeriesSummable` etc. -/
+scoped[LSeries.notation] notation:max "↗" f:max => fun n : ℕ ↦ (f n : ℂ)
+
+
 /-!
 ### Criteria for and consequences of summability of L-series