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But what is the Riemann zeta function? Visualizing analytic continuation

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Further reading 1

What becomes visible when you change representation? →An average, a spectrum and a geometric diagram each foreground a different structure. Before asking which view is intuitive, ask which comparison you need it to support.This video helps answer · When do an infinite series and a geometric answer agree?

Caption notes

The original zeta series has a domain of convergence. Analytic continuation adds a condition on how the function may extend beyond it; the original series need not converge at the new input.

Video or transcript source ↗
Original passages · 2
This function only makes sense when s is greater than 1
But what is the Riemann zeta function? Visualizing analytic continuation · ▶ 3:31–3:36
extending an analytic function in the only way possible that's still analytic
But what is the Riemann zeta function? Visualizing analytic continuation · ▶ 16:04–16:12

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