Associated with an irreducible curve of curve genus 
,
there are 
linearly independent integrals of the first
sort. The roots of the integrands are groups of the canonical
series, and every such group will give rise to exactly
one integral of the first sort.
Riemann's Integral Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 274, 1959.Referenced on Wolfram|Alpha
Riemann's Integral TheoremCite this as:
Weisstein, Eric W. "Riemann's Integral Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RiemannsIntegralTheorem.html