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- Kenji Koike, Annegret Weng
- Math. Comput.
- 2005

In this article we generalize the CM method for elliptic and hyperelliptic curves to Picard curves. We describe the algorithm in detail and discuss the results of our implementation.

- Kenji Koike
- 2008

Abstract. In this article we study the inverse of the period map for the family F of complex algebraic curves of genus 6 equipped with an automorphism of order 5. This is a family with 2 parameters, and is fibred over a certain type of Del Pezzo surace. The period satisfies the hypergeometric differential equation for Appell’s F1( 3 5 , 3 5 , 2 5 , 6 5 ) of… (More)

The latter theorem shows the relation of the (coefficients of the realized) elliptic curves corresponding to two isogenous torus C/Z + τZ and C/Z + 2τZ. So in general this theorem is referred as the isogeny formula for the Jacobi theta constants. Any way these two theorems are telling us a very interesting story concerned with AGM, periods of algebraic… (More)

In this paper we study the theta contants appeared in [S] those induced the modular function for the family of Picard curves C(ξ) given by (1). Our theta constants θk(u, v) (k = 0, 1, 2) , given by (3), are ”Neben type” modular forms of weight 1 defined on the complex 2-dimensional hyperball B, given by (2), with respect to a index finite subgroup Γθ of the… (More)

- Kenji Koike
- 2002

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.

- Kenji Koike
- 2002

Possible existence of “hot-sector generations” above the well known 3 generation bound is investigated on the basis of a model of leptons and quarks, which is based on the Harari and Shupe’s one. Our model predicts the existence of 3 + 1 generations above the ordinary “cold-sector” 3 generations. Majorana neutrinos are introduced to realize the heavy… (More)

- Bert van Geemen, Kenji Koike, Annegret Weng
- Finite Fields and Their Applications
- 2005

We explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex… (More)

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