Yukitaka Abe

activity

20152020

most citedMeromorphic function fields closed by partial derivatives

2 citations · 3 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2020

A transcendence result on elliptic functions using functions of two variables

Yukitaka Abe

Let $℘$ be a Weierstrass $℘$ -function with algebraic $g_{2}$ and $g_{3}$ , which has a non-zero real period $ω$ . We show that at least one of $π r$ and $℘ (ω r)$ is transcendental…

math.CV2019

A generalization of Riemann's theta functions for singular curves

Yukitaka Abe

Let $X$ be a compact Riemann surface of genus $g$ . Jacobi's inversion theorem states that the Abel-Jacobi map $φ : X^{(g)} ⟶ J (X)$ is surjective, where $X^{(g)}$ is th…

math.AG2019

Degenerate abelian function fields

Yukitaka Abe

Originally, an abelian function field is the field of meromorphic functions on the Jacobi variety J(X) of a compact Riemann surface X. It is generated by the fundamental abelian fu…

math.CV2018★ 2 cited

Meromorphic function fields closed by partial derivatives

Yukitaka Abe

We characterize meromorphic function fields closed by partial derivatives in n variables.

math.CV2017

Geometrically simple quasi-abelian varieties

Yukitaka Abe

We define the geometric simpleness for toroidal groups. We give an example of quasi-abelian variety which is geometrically simple, but not simple. We show that any quasi-abelian va…

math.CV2016★ 1 cited

Analytic study of singular curves

Yukitaka Abe

We study singular curves from analytic point of view. We give completely analytic proofs for the Serre duality and a generalized Abel's theorem. We also reconsider Picard varieties…