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**Abstract:**

On a Riemann surface there are relations among the
periods of holomorphic differential forms, called Riemann's relations. If one
looks carefully in Riemann's proof, one notices that he uses iterated integrals
(I will explain what that means.) What I have done is to generalize these
relations to relations among generating series of iterated integrals. Since it
is formulated in terms of generating series, it gives infinitely many relations
- one for each coefficient of the generating series. The degree one term gives
that the sum of the residues of a meromorphic differential form is zero. The
degree 2 term gives Riemann's relations. The new result is for the higher for
the higher degree terms, which give non-trivial relations among iterated
integrals.