11 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…
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…