Explicit Coleman Integration for Hyperelliptic Curves
نویسندگان
چکیده
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.
منابع مشابه
Coleman Integration for Even Degree Models of Hyperelliptic Curves
The Coleman integral is a p-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [8], we extend the Coleman integration algorithms in [2] to even degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.
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