If the difference between the order and the dimension of a series is less than the curve genus, then the series is special.
Special Series Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 253, 1959.Referenced on Wolfram|Alpha
Special Series TheoremCite this as:
Weisstein, Eric W. "Special Series Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpecialSeriesTheorem.html