Aiichi Yamasaki's Homepage

Preprints arXiv

• (with A.Hoshi) Norm one tori and Hasse norm principle, III: Degree 16 case. (arXiv:2404.01362, accompanying GAP code )
• (with A.Hoshi) Rationality problem for norm one tori for $A_5$ and ${\rm PSL}_2(\mathbb{F}_8)$ extensions. (arXiv:2309.16187, accompanying GAP code )
• (with A.Hoshi, K. Kanai) Hasse norm principle for M₁₁ and J₁ extensions. (arXiv:2210.09119, accompanying GAP code)
• (with A. Hoshi) Birational classification for algebraic tori. (arXiv:2112.02280, accompanying GAP code)
• (with A. Hoshi, Ming-chang Kang) An application of cohomological invariants (arXiv:1903.03750)
• Rationality problem of conic bundles. (arXiv:1408.2233)

Publications MathSciNet

• (with A. Hoshi) Rationality problem for norm one tori for dihedral extensions.
  Journal of Algebra 640 (2024) 368-384. (arXiv:2302.06231)
• (with A. Hoshi, K. Kanai) Norm one tori and Hasse norm principle, II: Degree 12 case.
  Journal of Number Theory 244 (2023) 84-110. (arXiv:2003.08253, accompanying GAP code)
• (with A. Hoshi, K. Kanai) Norm one tori and Hasse norm principle.
  Mathematics of Computation 91 (2022) 2431-2458. (arXiv:1910.01469, accompanying GAP code)
• (with A. Hoshi, M. Kang and H. Kitayama) A two-dimensional rationality problem.
  Manuscripta Mathematica 168 (2022) 423-437. (arXiv:1801.06616)
• (with A. Hoshi and M. Kang) Multiplicative Invariant Fields of Dimension ≤ 6.
  To appear in Memoirs of the American Mathematical Society. (arXiv:1609.04142, accompanying GAP code)
• (with A. Hoshi) Rationality problem for norm one tori.
  Israel Journal of Mathematics 241 (2021) 849-867. (arXiv:1811.01676, accompanying GAP code)
• (with S. Hasegawa and A. Hoshi) Rationality problems for norm one tori in small dimensions.
  Mathematics of Computation 89 (2020) 923-940. (arXiv:1811.02145, accompanying GAP code)
• (with A. Hoshi and M. Kang) Degree three unramified cohomology groups and Noether's problem for groups of order 243.
  Journal of Algebra 544 (2020) 262-301. (arXiv:1710.01958, accompanying GAP code)
• (with A. Hoshi and M. Kang) Relation modules of dihedral groups.
  Journal of Algebra 530 (2019) 368-401. (arXiv:1503.04543) (Old version:arXiv:1312.6738)
• (with A. Hoshi) Rationality problem for algebraic tori.
  Memoirs of the American Mathematical Society 248 (2017), no.1176, v+215 pp. (arXiv:1210.4525, accompanying GAP code)
• (with A. Hoshi and M. Kang) Degree three unramified cohomology groups.
  Journal of Algebra 458 (2016), 120-133. (arXiv:1503.08375)
• Negative solutions to three-dimensional monomial Noether problem.
  Journal of Algebra 370 (2012), 46-78. (accompanying GAP code) (Old version:arXiv:0909.0586v2)
• (with A. Hoshi and H. Kitayama) Rationality problem of three-dimensional monomial group asctios.
  Journal of Algebra 341 (2011), 45-108. (arXiv:0912.5259)
• Some Cases of Four Dimensional Linear Noether's Problem.
  Journal of Mathematical Society of Japan 62 (2010), no.4, 1273-1288.
• (with H. Kitayama) The rationality problem for four-dimensional linear actions.
  Journal of Mathematics, Kyoto University 49 (2009), no.2, 359-380.
• The structure of a complete valuation ring with an infinite residue field.
  Journal of Mathematics, Kyoto University 45 (2005), no.3, 633-644.
• Toward a generalization of strong approximation theorem to a general PF field.
  Journal of Mathematics, Kyoto University 42 (2002), no.3, 477-484.
• Inductive limit of general linear groups.
  Journal of Mathematics, Kyoto University 38 (1998), no.4, 769-779.
• Brauer Group of a Rational Function Field over a Perfect Field.
  Journal of Number Theory 65 (1997), no.2, 295-304.
• Cancellation of Lattices and Approximation Properties of Division Algebras.
  Journal of Mathematics, Kyoto University 36 (1996), no.4, 857-867.
• Strong Approximation Theorem for Division Algebras over R(X).
  Journal of Mathematical Society of Japan. 49 (1997), no.3, 455-467.