# Bilinear differential

From Encyclopedia of Mathematics

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