08/18/2022, 06:56 AM
(08/17/2022, 02:58 AM)JmsNxn Wrote: If you want to go down the Riemann surface route though. We should refer to this more broadly.
(08/17/2022, 02:58 AM)JmsNxn Wrote: Let's go down the rabbit hole, bo! I loved Leo's original thesis. And I loved the idea. The trouble I had, was that it was the image, and not the Riemann surface preimage.
No, I totally don't want to go that rabbit hole! This would be a lot of theory to digest, with possibly no effect on the questions we have - rather it would pose a lot of new questions! Remember, I am beyond my limit already ...
And I found already what I wanted. Its not just that you can say: well we doing everything multivalued (like when you draw a picture of arctan with stacked copies along y) and somehow some choice of branch will work - but it is rather the idea of (analytic) continuation that solves the puzzle - the graph is *one* continuous line, one does not need to care which branch cut gets glued to which other branch cut.
But what exactly you mean by Leo's original thesis?