Holomorphic Differentials As Functions of Moduli

Cover Holomorphic Differentials As Functions of Moduli
Holomorphic Differentials As Functions of Moduli
Lipman Bers
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"ri.^ : ■^- -"i. N.
it- •. •at.
:ir. O^ 'f'-'r- IT} 's&(T-tts), ^. Q 1 ^B q* nod'-'*' ?\nr -fi. ?i'r.
'•(S) '. I ■, :/'■ W 'lo :!^. Emc«I?> v^ts^/Zl' . II rj J.
iH - k - converges normally In M and its sum belongs ta ¥ . On the other hand, since D(t) Is a bounded Jordan domain and G(t) has a compact fundamental region. Theorem L|. In [I4. ] implies that, for a fixed 1, every element of W (t ) is of the form (3)« For q - 1 we shall show that every p. Belongs to W^ (i. E. That the ntrmalized Abel
...ian differentials are holomorphic functions of the mo dul i ) .
THEOREM III. The functions p (z, t), / c. (t) 5. (z, t) ■^ ' j'^l J iJ ■. ...
where the c. Are holomorphic, O^W^, and the 0. Are elements of W^. We first choose so that o(z, t ) vanishes at kg-k points z.


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