Definition talk:Riemann Zeta Function

This approach doesn't work. The equivalence proof itself uses theorems and definitions about $\zeta$ already. In fact it doesn't look like it was ever the intention to do it this way, a page that should've been called Analytic Continuations of Riemann Zeta Function became Equivalence of Definitions of Riemann Zeta Function, and then those formulas were given the status of definitions, but shouldn't have been.

Clean proposal: --barto (talk) (contribs) 17:10, 14 November 2017 (EST)
 * Define $\zeta$ for $\sigma=\Re (s)>1$ only, series + product.
 * Construct analytic continuations, some for $\sigma>0$ etc, others for $\sigma>-\infty$. Proofs on separate pages.
 * Overview page Analytic Continuations of Riemann Zeta Function, with one-line equivalence proof using Uniqueness of Analytic Continuation.
 * Add a section "Analytic continuation" here (like it was long ago), extending the definition $\zeta$ by any (don't specify) of the analytic continuations, at that point already proved to be equivalent.