Publication List of Takaaki KAGAWA
Thesis
Elliptic curves with everywhere good reduction over real quadratic fields
(pdf)
Papers
- Determination of elliptic curves with everywhere good reduction over real quadratic fields, II, International Journal of Algebra 16 (2022), 219-240.
- The Diophantine equation X3=u+v over real quadratic fields,II, Tokyo J. Math. 44 (2021), 507-513
- The Diohphntine equtaion X3=1+9v over quadratic fields, Mem. Inst. Sci. Engrg. Ritsumeikan Univ. 77 (2018), 1-3
- Torsion groups of elliptic curves with everywhere good reducion over quadratic fields, International Journal of Algebra 10 (2016), 461-467.
- The Diohphantine eqation X3=u+v over real quadratic fields,
Bull. Pol. Acad. Sci. Math. 59 (2011), 1-9
- The Diohphantine eqation X3=u+27v over real quadratic fields,
Tokyo J. Math. 33 (2010), 159-163.
- Elliptic curves over $Q(\sqrt2)$ with good reduction outside $\sqrt2$, Mem. Inst. Sci. Engrg. Ritsumeikan Univ. 59, (2000), 63-79 (2001).
- Determination of elliptic curves with everywhere good reduction over real quadratic fields $Q(\sqrt{3p})$,
Acta Arith. 96 (2001), 231-245.
(Remix version.)
- Nonexistence of elliptic curves having everywhere good reduction
and cubic discriminant,
Proc. Japan Acad., Ser. A 76 (2000), 141-142.
- Determination of elliptic curves with everywhere good reduction over real quadratic fields. Arch. Math., 73 (1999), 25-32. (pdf)
- Squares in Lucas sequences and some Diophantine equations (with Nobuhiro Terai),Manuscripta Math. 96 (1998), 195-202. (pdf)
- Determination of elliptic curves with everywhere good reduction over $Q(\sqrt{37})$,
Acta Arith. 83 (1998), 253-269.
- Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields (with Masanari Kida), J. Number Theory 66 (1997), 201-210.
- The Hasse norm principle for the maximal real subfields of cyclotomic fields,
Tokyo J. Math. 18 (1995), 221-229.
Talks
- The Diophantine equation X^3=u+v, Symposim of Number Theory
(@ Sci. and Eng. Waseda Univ.)
Slides for the talk
- The Diophantine equation X^3=u+27v over real quadratic fields,
Matsue Number Theory Symposium @ Shimane Univ.
- Computation of integral points over an real quadratic fields,
and determitation of elliptic curves with everywhere good reduction,
Symposium of Number Theory (@Sci. and Eng. Waseda University)
- Elliptic curves with everywhere good reduction over real quadratic fields,
symposium "Algebra and Computational Number Theory"
(@Tokyo Metroporitain University)
- Determination of elliptic curves with everywhere good reduction over certain real quadratic fields,
syposium "Algebraic number fields and related topics (@Kyoto Univ.).
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