Coleman integration for even-degree models of hyperelliptic curves
نویسندگان
چکیده
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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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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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2015
ISSN: 1461-1570
DOI: 10.1112/s1461157015000029