If I were to manipulate the zeta function in a 'new way' would I end up with an analytic continuation that is equal to the one know or something completely new for values less than 1 and complex numbers?
2026-04-06 15:20:15.1775488815
Is there only one analytic continuation of the Riemann zeta function?
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Analytic continuations to a specified domain are always unique (due to the identity theorem for holomorphic functions).