Explicit Coleman integration for hyperelliptic curves

Details Explicit Coleman integration for hyperelliptic curves Explicit Coleman integration for hyperelliptic curves

2010-04-28

arxiv.org/abs/1004.4936v2

Mathematics

Number Theory

16 pages; v2: final submission to ANTS 9

Scientific paper

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.

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