I’m basically a layman trying to understand the Riemann Hypothesis, and in my journey so far I’ve made it past the zeta function, somewhat understand the part about using complex numbers as exponents, and up to the part about ‘extending the domain of an infinite series using analytic continuation’.
How exactly are mathematicians finding values for diverging series using it? Are they basically winging it by using geometry or is there a specific way?
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The spirit: expanding the domain of an analytic function from R to C that also preserves the analyticity of the function in C.
Example: e^x to e^z
this preserves analyticity, because we have the famous identity:
e^iy = cos y + i sin y
Generalizing the idea, it’s an expansion of domain from X to Y, preserving the analyticity.
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