Notes on three formulas of Abel

Cox, David

doi:10.1090/bull/1865

Notes on three formulas of Abel
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by David A. Cox;

Bull. Amer. Math. Soc. 62 (2025), 481-536

DOI: https://doi.org/10.1090/bull/1865

Published electronically: April 29, 2025

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Abstract:

These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to residues and partial fractions. The third formula arises from the first two and is related to the genus and lattice points in the Newton polygon.

References

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Notes on three formulas of Abel
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