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Coleman integration for even-degree models of hyperelliptic curves

Part of: Algebraic number theory: local and $p$-adic fields Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  01 April 2015

Jennifer S. Balakrishnan
Jennifer S. Balakrishnan*
Affiliation:
Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom email [email protected]

Abstract

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The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

MSC classification

Primary: 11S80: Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
Secondary: 14G22: Rigid analytic geometry
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 258 - 265
Copyright
© The Author 2015 

References

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