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.
|||M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)|
Bilinear differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_differential&oldid=46059