scholarly journals Errata: The coincidence of fields of Moduli for non-hyperelliptic curves and for their Jacobian varieties (Nagoya Math. J., Vol. 82 (1981), 57–82)

1986 ◽  
Vol 103 ◽  
pp. 161-161
Author(s):  
Tsutomu Sekiguchi
Keyword(s):  
Hyperelliptic Curves ◽  
Nagoya Math ◽  
Jacobian Varieties ◽  
Fields Of Moduli

scholarly journals The coincidence of fields of moduli for non-hyperelliptic curves and for their jacobian varieties

1981 ◽  
Vol 82 ◽  
pp. 57-82 ◽  
Author(s):  
Tsutomu Sekiguchi
Keyword(s):  
Abelian Varieties ◽  
Hyperelliptic Curves ◽  
Jacobian Varieties ◽  
Axiomatic Treatment ◽  
Fields Of Moduli

The notion of fields of moduli introduced first by Matsusaka [8] has been developed by Shimura [12] exclusively in the area of polarized abelian varieties. Later Koizumi [7] gave an axiomatic treatment for the notion.

scholarly journals Character sums, Gaussian hypergeometric series, and a family of hyperelliptic curves

2016 ◽  
Vol 12 (08) ◽  
pp. 2173-2187 ◽  
Author(s):  
Mohammad Sadek
Keyword(s):  
Hypergeometric Series ◽  
Hyperelliptic Curves ◽  
Character Sums ◽  
Rational Points ◽  
Quadratic Character ◽  
Jacobian Varieties ◽  
Gaussian Hypergeometric Series

We study the character sums [Formula: see text] [Formula: see text] where [Formula: see text] is the quadratic character defined over [Formula: see text]. These sums are expressed in terms of Gaussian hypergeometric series over [Formula: see text]. Then we use these expressions to exhibit the number of [Formula: see text]-rational points on families of hyperelliptic curves and their Jacobian varieties.

FORMAL GROUPS OF JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES

2010 ◽  
Vol 06 (07) ◽  
pp. 1701-1716
Author(s):  
FUMIO SAIRAIJI
Keyword(s):  
Elliptic Curves ◽  
Characteristic Zero ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Formal Groups ◽  
Jacobian Varieties ◽  
Explicit Constructions ◽  
Modulo P

Let k be a field of characteristic zero. In this paper, we discuss two explicit constructions of the formal groups Ĵ of the Jacobian varieties J of hyperelliptic curves C over k. Our results are generalizations of the classical constructions of formal groups of elliptic curves. As an application of our results, we may decide the type of bad reduction of J modulo p when C is a hyperelliptic curve over ℚ.

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.

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