1 citations · 1 across the 13 of their papers we have counts for
14 papers
Algebraic Quantum Intelligence: A New Framework for Reproducible Machine Creativity
Kazuo Yano, Jonghyeok Lee, Tae Ishitomi +26
Large language models (LLMs) have achieved remarkable success in generating fluent and contextually appropriate text; however, their capacity to produce genuinely creative outputs…
Periods modulo of integer sequences associated with division polynomials of genus curves
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita +2
We study an integer sequence associated with Cantor's division polynomials of a genus 2 curve having an integral point. We show that the reduction modulo of such a sequence is…
The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields
Kenichi Bannai, Hohto Bekki, Kei Hagihara +3
In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally…
Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves
Toshiro Hiranouchi, Tatsuya Ohshita
In this article, we study a relation between certain quotients of ideal class groups and the cyclotomic Iwasawa module of the Pontrjagin dual of the fine Selmer group of…
The arithmetic of a twist of the Fermat quartic
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We study the arithmetic of the twist of the Fermat quartic defined by which has no -rational point. We calculate the Mordell--Weil group of the Ja…
The local-global property for bitangents of plane quartics
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita +2
We study the arithmetic of bitangents of smooth quartics over global fields. With the aid of computer algebra systems and using Elsenhans--Jahnel's results on the inverse Galois pr…
Asymptotic lower bound of class numbers along a Galois representation
Tatsuya Ohshita
Let T be a free Z_p-module of finite rank equipped with a continuous Z_p-linear action of the absolute Galois group of a number field K satisfying certain conditions. In this artic…
On infinite extensions of Dedekind domains, upper semicontinuous functions and the ideal class semigroups
Tatsuya Ohshita
In this article, we study the monoid of fractional ideals and the ideal class semigroup of an arbitrary given one dimensional normal domain O obtained by an infinite integral exten…
On algorithms to obtain linear determinantal representations of smooth plane curves of higher degree
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representativ…
Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We use explicit methods to study the 4-torsion points on the Jacobian variety of the Fermat quartic. With the aid of computer algebra systems, we explicitly give a basis of the gro…
Euler systems for Galois deformations and the pseudo-isomorphism class of the dual of fine Selmer groups
Tatsuya Ohshita
In this article, we study the pseudo-isomorphism class of the dual fine Selmer group attached to a -adic Galois deformation whose deformation ring is isomorphic to the r…
On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units II
Tatsuya Ohshita
In our previous work, by using Kolyvagin derivatives of elliptic units, we constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i become "upper bounds" of th…
On the higher Fitting ideals of Iwasawa modules of ideal class groups over real abelian fields
Tatsuya Ohshita
Kurihara established a refinement of the minus-part of the Iwasawa main conjecture for totally real number fields using the higher Fitting ideals. In this paper, by using Kurihara'…
The Euler system of cyclotomic units and higher Fitting ideals
Tatsuya Ohshita
Kurihara established a refinement of the minus-part of the Iwasawa main conjecture for totally real number fields using the higher Fitting ideals. In this paper, we study the highe…