Explicit coleman integration for hyperelliptic curves

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Abstract

Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage. © 2010 Springer-Verlag Berlin Heidelberg.

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Balakrishnan, J. S., Bradshaw, R. W., & Kedlaya, K. S. (2010). Explicit coleman integration for hyperelliptic curves. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 16–31). https://doi.org/10.1007/978-3-642-14518-6_6

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