40 citations · 87 across the 17 of their papers we have counts for
17 papers
Arithmetic over the Gaussian Number Field on a Certain Family of Elliptic Curves with Complex Multiplication
Yoshihiro Ônishi, Fumio Sairaiji
This work is a sequel of a previous work of one of the authors (Y.Ô), which treated certain congruence relation between an elliptic Gauss sum and a coefficient of power series expa…
Hurwitz integrality of power series expansion of the sigma function for a plane curve
Yoshihiro Ônishi
This paper shows Hurwitz integrality of the coefficients of expansion at the origin of the sigma function \(σ(u)\) associated to a certain plane curve which should be called a plan…
Some New Addition Formulae for Weierstrass Elliptic Functions
J. Chris Eilbeck, Matthew England, Yoshihiro Ônishi
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit…
Prime form and sigma function
John Gibbons, Shigeki Matsutani, Yoshihiro Onishi
In this article, we study some cyclic curves given by . We give an expression for the prime form $\cE(P,Q)$, where $(P,…
Universal elliptic functions
Yoshihiro Onishi
For the elliptic curve defined by the most general form , we show the power series expansion of Weierstsass sigma function $σ(u…
Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type
J. C. Eilbeck, S. Matsutani, Y. Onishi
We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of genus one and two with many automorphisms. In the genus one case we find new…