Papers and Talks

[Japanese/English]

Publications

1. A note on the Selmer group of the elliptic curve y²=x³+Dx, Proc. Japan Acad. 77A (2001), 122-125.

2. Calculation of Selmer groups of elliptic curves with rational 2-torsions and \theta-congruent number problem, Comment. Math. Univ. St. Paul. 50 (2001), 147-172.

3. (with S. Shibata) All numbers whose positive divisors have integral harmonic mean up to 300, Math. Comp. 73 (2004), 475-491.

4. (with Y. Chishiki, Y. Ohno) On the largest prime divisor of an odd harmonic number, Math. Comp. 76 (2007), 1577-1587.

5. Upper bounds for unitary perfect numbers and unitary harmonic numbers, Rocky Mountain J. Math. 37, no. 5 (2007), 1557-1576.

6. (with K. Okeya) All harmonic numbers less than 10¹⁴, Japan J. Indust. Appl. Math. 24 (2007), 275-288. details

7. (with Y. Ohno) Odd perfect numbers have a prime factor exceeding 10⁸, Math. Comp. 77 (2008), 1859-1868. details

Talks

1. (with K. Okeya) An algorithm to compute harmonic numbers, Japan Society for Industrial and Applied Mathematics, JANT8, at Tokyo Metropolitan Univ., Sep. 5, 2002. slide

2. Calculation of Selmer groups of elliptic curves with a rational 2-torsion, Diophantine Problems and Analytic Number Theory, at Research Institute for Mathematical Sciences, Kyoto Univ., Oct. 24, 2002.

3. On Ore's harmonic numbers, Seminar Series at University of Technology, Sydney, Sep. 20, 2004. slide

4. Odd graphs and Selmer groups of certain elliptic curves, AC2005, at Tokyo Metropolitan Univ., Nov. 17, 2005.

Others

1. A Study on the Selmer Groups of the Elliptic Curves with a Rational 2-torsion, Kyushu University, PhD Thesis (2002). pdf.

2. Calculation of Selmer groups of elliptic curves with rational 2-torsion, Diophantine Problems and Analytic Number Theory, Surikaisekikenkyusho Kokyuroku, 1319, 183-192, (2003).

3. Odd graphs and Selmer groups of certain elliptic curves, Algebra and Computation, report collection no. 6 (2005), 10 pp, availapble at the ftp site.

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