30 citations · 68 across the 8 of their papers we have counts for
7 papers · 1 filter
Torsion points on Jacobian varieties via Anderson's p-adic soliton theory
Shinichi Kobayashi, Takao Yamazaki
Anderson introduced a -adic version of soliton theory. He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certai…
The Kronecker limit formulas via the distribution relation
Kenichi Bannai, Shinichi Kobayashi
In this paper, we give a proof of the classical Kronecker limit formulas using the distribution relation of the Eisenstein-Kronecker series. Using a similar idea, we then prove …
Integral structures on -adic Fourier theory
Kenichi Bannai, Shinichi Kobayashi
In this article, we give an explicit construction of the -adic Fourier transform by Schneider and Teitelbaum, which allows for the investigation of the integral property. As an…
On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves
Kenichi Bannai, Shinichi Kobayashi, Takeshi Tsuji
In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the…
Algebraic theta functions and Eisenstein-Kronecker numbers
Kenichi Bannai, Shinichi Kobayashi
In this paper, we give an overview of our previous paper concerning the investigation of the algebraic and -adic properties of Eisenstein-Kronecker numbers using Mumford's theor…
An elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves
Shinichi Kobayashi
We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.
Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers
Kenichi Bannai, Shinichi Kobayashi
We study the properties of Eisenstein-Kronecker numbers, which are related to special values of Hecke -function of imaginary quadratic fields. We prove that the generating funct…