Book recs please - complex analysis, riemann surfaces, multi-valued functions

[bb16]

Hi everyone, hope this is the right place to put this :)

I have just finished "Theory of Functions" Vol. 1 & 2 by Konrad Knopp. I'd like to continue with a book that picks up where the second volume it left off. (Especially would be nice is a more "modern" book)

The second volume is about multi-valued functions, riemann surfaces, the analytic configuration given rise two by 2-d polynomials, etc.

Ideally, it would be a book that assumes a working comfort with graduate level complex analysis and algebra, but is somewhat self contained (i.e. doesn't expect complete mastery of, say, algebraic topology). I'm open to all suggestions though.

Thanks :)

edit: links to internet resources would also be highly appreciated :)

 

[fresh_42]

Quite a broad question, esp. if you don't know Knopp. I like Hewitt / Stromberg Real And Abstract Analysis but it might not be modern enough for you. It has a measure theoretic emphasis.

I have long lists of references at the end of these articles:
https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/#toggle-id-2https://www.physicsforums.com/insights/pantheon-derivatives-part-v/#toggle-id-2

 

[Infrared]

Miranda's book Algebraic Curves and Riemann Surfaces might be what you are looking for.