Publication List of Takaaki KAGAWA

$B3X0LO@J8(B$B!'(B Elliptic curves with everywhere good reduction over real quadratic fields (pdf)

Papers
1. Determination of elliptic curves with everywhere good reduction over real quadratic fields, II, International Journal of Algebra 16 (2022), 219-240.
2. The Diophantine equation X3=u+v over real quadratic fields,II, Tokyo J. Math. 44 (2021), 507-513.
3. The Diohphntine equtaion X3=1+9v over quadratic fields, Mem. Inst. Sci. Engrg. Ritsumeikan Univ. 77 (2018), 1-3.
4. Torsion groups of elliptic curves with everywhere good reducion over quadratic fields, International Journal of Algebra 10 (2016), 461-467.
5. The Diohphantine eqation X3=u+v over real quadratic fields, Bull. Pol. Acad. Sci. Math. 59 (2011), 1-9.
6. The Diohphantine eqation X3=u+27v over real quadratic fields, Tokyo J. Math. 33 (2010), 159-163.
7. Elliptic curves over $Q(\sqrt2)$ with good reduction outside $\sqrt2$, Mem. Inst. Sci. Engrg. Ritsumeikan Univ. 59, (2000), 63-79 (2001).
8. Determination of elliptic curves with everywhere good reduction over real quadratic fields $Q(\sqrt{3p})$, Acta Arith. 96 (2001), 231-245.
(Remix version.)
9. Nonexistence of elliptic curves having everywhere good reduction and cubic discriminant, Proc. Japan Acad., Ser. A 76 (2000), 141-142.
10. Determination of elliptic curves with everywhere good reduction over real quadratic fields. Arch. Math., 73 (1999), 25-32. (pdf)
11. Squares in Lucas sequences and some Diophantine equations (with Nobuhiro Terai), Manuscripta Math. 96 (1998), 195-202. (pdf)
12. Determination of elliptic curves with everywhere good reduction over $Q(\sqrt{37})$, Acta Arith. 83 (1998), 253-269.
13. Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields (with Masanari Kida), J. Number Theory 66 (1997), 201-210.
14. The Hasse norm principle for the maximal real subfields of cyclotomic fields, Tokyo J. Math. 18 (1995), 221-229.
Preprint

No paper is a good news?

$B%7%s%]%8%&%9V1i(B 1. $Be;j$k=j(Bgood reduction$B$r;}$DBJ1_6J@~$N7hDj$K$D$$F!"(B BBh(B12B2sKLN&?tO@8&5f=82q!J1w6bBtBg3X%5%F%i%%H%W%i%6!K(B 2. B!H(BThe Diophantine equation X^3=u+vB!I@0?tO@%7%s%]%8%&%(B B!J1w(B BAa0pEDBg3XM}9)3X=Q1!!K(B Slides for the talk BJs9p=8!JF|K\8l(B pdfB!K(B 3. BeNITDjJ}Dx<0(B X^3=u+27v BKD$$$F!">>9>?tO@8&5f=82q(B $B!J1w(B $BEg:,Bg3XAm9gM}9)3XIt!K!#(Bpdf
4. $Be$NBJ1_6J@~$N@0?tE@$N7W;;(B, $B$*$h$S<+L@$JF3 $BC"$74V0c$$B?$7(B. $BD{@5HG$O(B$B$3$A$i$+$i(B$B!K(B 5. $Be;j$k=j(Bgood reduction$B$r;}$DBJ1_6J@~(B, $B%7%s%]%8%&%!VBe?t3X$H7W;;!W(B($B1w(B $BEl5~ETN)Bg3X(B)($BJs9p=8!'(B$B$3$A$i(B$B$h$jF~$B$3$A$i$+$i(B)
6. Determination of elliptic curves with everywhere good reduction over certain real quadratic fields, $B8&5f=82q!VBe?tE*@0?tO@$H$=$N<~JU$N8&5f!W(B($B1w(B $B5~ETBg3X?tM}2r@O8&5f=j(B). ($BJs9p=8!'(B$B5~ETBg3X?tM}2r@O8&5f=j9V5fO?(B 998 (1997), 67$B!](B77.)
$B3X2q9V1i(B 1. Nonexistence of elliptic curves with everywhere good reduction over certain real quadratic fields, 1999$BG/EYF|K\?t3X2q=U5(Am9gJ,2J2q!J1w(B $BAa0pEDBg3XM}9)3XIt!K(B 2. $Be$NBJ1_6J@~$N(BMordell-Weil$B72$H@0?tE@$N7W;;!"5Z$S$=$N1~MQ!"(B1998$BG/EYF|K\?t3X2q=)5(Am9gJ,2J2q!J1w(B $BBg:eBg3X!K(B
3. Elliptic curves with everywhere good reduction over real quadratic fields, 1997$BG/EYF|K\?t3X2q=)5(Am9gJ,2J2q!J1w(B $BEl5~Bg3X!K(B
4. Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields $B!J(B$BLZED2m@.;a(B$B$H$N6&F18&5f!K!"(B1997$BG/EYF|K\?t3X2q=U5(Am9gJ,2J2q!J1w(B $B?.=#Bg3X!K(B 5. Squares in Lucas sequences and some Diophantine equations ($B;{0f?-9@;a$H$N6&F18&5f(B), 1997$BG/EYF|K\?t3X2q=U5(Am9gJ,2J2q!J1w(B $B?.=#Bg3X!K(B
6. $BITDjJ}Dx<0(B 4x^4-37y^2=-1 $B$H$=$N1~MQ(B, 1996$BG/EYF|K\?t3X2q=)5(Am9gJ,2J2q(B ($B1w(B $BEl5~ETN)Bg3X(B).
7. Q(\sqrt N) (N=29,37,41)$B>e;j$k=j(Bgood reduction$B$r;}$DBJ1_6J@~$N7hDj(B, 1996$BG/EYF|K\?t3X2q=)5(Am9gJ,2J2q!J1w(B $BEl5~ETN)Bg3X!K(B
8. $B1_J,BN$N:GBg $B2J8&Hq(B 2002$BG/EY!A(B2004$BG/EY(B $BBJ1_6J@~$H4XO"$9$kITDjJ}Dx<0$N8&5f!JBeI=!K(B
2001$BG/EY!A(B2002$BG/EY(B  $BEye$NC1=c72

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