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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
0
votes
Holomorphic union of sets
Certainly not. If you take U, V to be small neighborhoods of distinct points this will fail. Are you sure this is what you need?
6
votes
Analytic continuation of the double sum $\sum_{n,m\ge0}x^ny^mt^{nm}$
I think you can do the following (I haven't checked convergence carefully, so don't trust me too much). Write $a = \frac{m+n}{2}, b = \frac{m-n}{2}.$ Then $mn = a^2-b^2.$ Now (let's ignore indetermina …