Wednesday, 30 November 2011

cv.complex variables - Power series for meromorphic differentials on compact Riemann surfaces

Suppose I have a compact Riemann surface of g>1 given by the quotient H/Gamma where I do know Gamma explicit. Is there a way to write down the power series of meromorphic functions, differentials, quadratic differentials, and so on explicitly if one does know these sections explicitly (for example in a hyperelliptic picture of the surface).
I know that there is the subject of automorphic forms, but the literature I have seen about this concentrates on modular groups. Moreover it is typically written for number theorists.
Is there literature for compact surfaces (for example Y2=Z61), and maybe readable for geometers.



Thank you.

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