scholarly journals Deterministic Encoding and Hashing to Odd Hyperelliptic Curves

2010 ◽  
pp. 265-277 ◽  
Author(s):  
Pierre-Alain Fouque ◽  
Mehdi Tibouchi
Keyword(s):  
Hyperelliptic Curves

scholarly journals Coleman integration for even-degree models of hyperelliptic curves

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Hyperelliptic Curves ◽  
Open Book ◽  
Line Integral ◽  
Book Series ◽  
Numerical Examples ◽  
Lecture Notes ◽  
Integration Algorithms ◽  
Mathematical Sciences

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.

scholarly journals Integral points on hyperelliptic curves

2008 ◽  
Vol 2 (8) ◽  
pp. 859-885 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek ◽  
Michael Stoll ◽  
Szabolcs Tengely
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

scholarly journals The realization of hyperelliptic curves through endomorphisms of Kronecker modules

2010 ◽  
Vol 432 (5) ◽  
pp. 1189-1217
Author(s):  
Frank Okoh ◽  
Frank Zorzitto
Keyword(s):  
Hyperelliptic Curves
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