Bilinear differential

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An analytic differential on a Riemann surface, depending on two points $ P $ and $ Q $, and having the form

$$ f (z, \zeta ) dz d \zeta , $$

where $ z $ and $ \zeta $ are local uniformizing parameters in a neighbourhood of $ P $ and $ Q $ respectively, and $ f(z, \zeta ) $ is an analytic function of $ z $ and $ \zeta $. Bilinear differentials are used to express many functionals on a finite Riemann surface.


[1] M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)
How to Cite This Entry:
Bilinear differential. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article