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May 16, 2023 at 7:37 comment added Alexandre Eremenko Suppose you have two forms with the same poles and principal parts. Then their difference is a holomorphic form. Holomorphic forms make a vector space of dimension $g$, and a basis in this space is obtained by the forms whose $a$-periods form the unit matrix. This gives you a uniqueness condition.
May 15, 2023 at 7:43 history edited YCor CC BY-SA 4.0
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May 15, 2023 at 3:24 history edited zapkm CC BY-SA 4.0
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May 15, 2023 at 3:17 history asked zapkm CC BY-SA 4.0