English
For a Dirichlet character χ, the L-function LFunction χ is defined as the meromorphic function extending the Dirichlet series ∑ χ(n)/n^s; more precisely, LFunction χ s = ZMod.LFunction χ s.
Русский
Для персонажа Дирichле χ функция LFunction χ есть величина, являющаяся мероморфной продолжением ряда ∑ χ(n)/n^s; точнее LFunction χ s = ZMod.LFunction χ s.
LaTeX
$$LFunction χ s = ZMod.LFunction χ s$$
Lean4
/-- The unique meromorphic function `ℂ → ℂ` which agrees with `∑' n : ℕ, χ n / n ^ s` wherever the
latter is convergent. This is constructed as a linear combination of Hurwitz zeta functions.
Note that this is not the same as `LSeries χ`: they agree in the convergence range, but
`LSeries χ s` is defined to be `0` if `re s ≤ 1`.
-/
@[pp_nodot]
noncomputable def LFunction (χ : DirichletCharacter ℂ N) (s : ℂ) : ℂ :=
ZMod.LFunction χ s
