# 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)
How to Cite This Entry:
Bilinear differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_differential&oldid=46059
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article