pith. machine review for the scientific record. sign in
theorem proved term proof

analyticAt_riemannZeta

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 546theorem analyticAt_riemannZeta {s : ℂ} (hs : s ≠ 1) :
 547    AnalyticAt ℂ riemannZeta s := by

proof body

Term-mode proof.

 548  have hdiff : DifferentiableOn ℂ riemannZeta {(1 : ℂ)}ᶜ :=
 549    fun z hz => (differentiableAt_riemannZeta hz).differentiableWithinAt
 550  exact hdiff.analyticAt (isOpen_compl_singleton.mem_nhds hs)
 551
 552/-- `zetaReciprocal` is meromorphic at every point of the strip (away from `s=1`).
 553This follows from `riemannZeta` being analytic at `s ≠ 1` and the inverse
 554of a meromorphic function being meromorphic. -/

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (13)

Lean names referenced from this declaration's body.