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Explicit Coleman Integration for Hyperelliptic Curves
"... Abstract. Coleman’s theory of padic integration figures prominently in several numbertheoretic applications, such as finding torsion and rational points on curves, and computing padic regulators in Ktheory (including padic heights on elliptic curves). We describe an algorithm for computing Cole ..."
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Cited by 8 (7 self)
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Coleman integrals on hyperelliptic curves, and its implementation in Sage. 1
COLEMAN INTEGRATION FOR EVEN DEGREE MODELS OF HYPERELLIPTIC CURVES
"... Abstract. The Coleman integral is a padic 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 numerica ..."
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Abstract. The Coleman integral is a padic 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
Iterated Coleman integration for hyperelliptic curves
 In Algorithmic number theory (ANTS X
, 2012
"... Abstract. The Coleman integral is a padic line integral. Double Coleman integrals on elliptic curves appear in Kim’s nonabelian Chabauty method, the first numerical examples of which were given by the author, Kedlaya, and Kim [3]. This paper describes the algorithms used to produce those examples, ..."
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Cited by 4 (4 self)
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Abstract. The Coleman integral is a padic line integral. Double Coleman integrals on elliptic curves appear in Kim’s nonabelian Chabauty method, the first numerical examples of which were given by the author, Kedlaya, and Kim [3]. This paper describes the algorithms used to produce those examples
ON HYPERELLIPTIC CURVES
"... Abstract. We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have often found this to be the case even w ..."
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Abstract. We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have often found this to be the case even
Integral points on hyperelliptic curves
 ALGEBRA NUMBER THEORY
, 2008
"... Let C: Y² = anX n + · · · + a0 be a hyperelliptic curve with the ai rational integers, n ≥ 5, and the polynomial on the right irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C an ..."
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Cited by 3 (1 self)
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Let C: Y² = anX n + · · · + a0 be a hyperelliptic curve with the ai rational integers, n ≥ 5, and the polynomial on the right irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C
Rational points on Jacobians of hyperelliptic curves
"... Abstract. We describe how to prove the MordellWeil theorem for Jacobians of hyperelliptic curves over Q and how to compute the rank and generators for the MordellWeil group. ..."
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Abstract. We describe how to prove the MordellWeil theorem for Jacobians of hyperelliptic curves over Q and how to compute the rank and generators for the MordellWeil group.
Explicit formulas for real hyperelliptic curves of genus 2
 in affine representation, in “International Workshop on the Arithmetic of Finite Fields – WAIFI 2007,” Lect. Notes Comput. Sci
, 2007
"... Abstract. In this paper, we present for the first time efficient explicit formulas for arithmetic in the degree 0 divisor class group of a real hyperelliptic curve. Hereby, we consider real hyperelliptic curves of genus 2 given in affine coordinates for which the underlying finite field has characte ..."
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Cited by 6 (2 self)
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Abstract. In this paper, we present for the first time efficient explicit formulas for arithmetic in the degree 0 divisor class group of a real hyperelliptic curve. Hereby, we consider real hyperelliptic curves of genus 2 given in affine coordinates for which the underlying finite field has
THE HARMONIC VOLUMES OF HYPERELLIPTIC CURVES
, 2005
"... Abstract. We determine the harmonic volumes for all the hyperelliptic curves. This gives a geometric interpretation of a theorem established by A. Tanaka [10]. 1. ..."
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Abstract. We determine the harmonic volumes for all the hyperelliptic curves. This gives a geometric interpretation of a theorem established by A. Tanaka [10]. 1.
Results 1  10
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