Bilinear differential

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.

References

[1]	M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)