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Ishitsuka Yasuhiro Last modified date:2021.06.15



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Homepage
https://kyushu-u.pure.elsevier.com/en/persons/yasuhiro-ishitsuka
 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
PhD(Science)(Kyoto University)
Country of degree conferring institution (Overseas)
Yes
Field of Specialization
Arithmetic invariant theory, Diophantine geometry
ORCID(Open Researcher and Contributor ID)
0000-0002-4461-6152
Total Priod of education and research career in the foreign country
00years00months
Research
Research Interests
  • Arithmetic invariant theory of exponential sums
    keyword : Arithmetic invariant theory, explicit arithmetic geometry
    2017.05.
Academic Activities
Papers
1. 石塚 裕大, A positive proportion of cubic curves over Q admit linear determinantal representations, Journal of the Ramanujan Mathematical Society, 32, 3, 231-257, 2017.09.
2. Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic, International Journal of Number Theory, 10.1142/s1793042120500451, 16, 04, 881-905, 2020.05, We use explicit methods to study the [Formula: see text]-torsion points on the Jacobian variety of the Fermat quartic. With the aid of computer algebra systems, we explicitly give a basis of the group of [Formula: see text]-torsion points. We calculate the Galois action, and show that the image of the mod [Formula: see text] Galois representation is isomorphic to the dihedral group of order [Formula: see text]. As applications, we calculate the Mordell–Weil group of the Jacobian variety of the Fermat quartic over each subfield of the [Formula: see text]th cyclotomic field. We determine all of the points on the Fermat quartic defined over quadratic extensions of the [Formula: see text]th cyclotomic field. Thus, we complete Faddeev’s work in 1960..