Andrew Adler. Extensions of non-standard models of number theory. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 15 (1969), pp. 289–290. - Haim Gaifman. A note on models and submodels of arithmetic. Conference in mathematical logic—London '70, edited by Wilfrid Hodges, Lecture notes in mathematics, no. 255, Springer-Verlag, Berlin, Heidelberg, and New York, 1972, pp. 128–144.

1975 ◽  
Vol 40 (2) ◽  
pp. 244-245
Author(s):  
C. Smorynski
2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan

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.


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