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have added a tad more to the Properties-section at Riemann zeta function.
I have added various further illuminating (hopefully) details to the proof here of how the Riemann zeta function relates to the Jacobi theta function via adelic integration.
(This is pretty neat, I find. I learned this from Ivan Fesenko. But I gather it is standard in the field. Is this explicitly already in Tate’s thesis?)
Is this explicitly already in Tate’s thesis?
Yes. Though he treats more general case of twisted zeta functions and you have to substitute the special case of the idelic character corresponding to the Riemann case. See also the Garrett’s lectures at Iwasawa-Tate theory for some details for the several special cases like the Riemann and Dirichlet zeta functions.
Thanks. Those lecture notes Garrett 11 are pretty useful as a review.
Preprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function:
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