I was a Global COE PD at Department of Mathematics at Kyoto University.

2000, Faculty of Science, Kyoto University
2004, Department of Mathematics at Kyoto University
2009/4-2013/3, GCOE-PD at Department of Mathematics at Kyoto University
2010/10-2012/3, Part-time teacher at Kyoto University(Additional)
2012/8- Part-time teacher at CJLC of Osaka University(Additional)
2013/4-, Part-time teacher at Kyoto Kyoiku University(Additional)

e-mail: y64k at chive.ocn.ne.jp (at should be replaced by @)

My Interests

I am interested in easily stated problems in number theory and discrete mathematics. Many of such problems are formulated and discussed by elementary number theory, analytic number theory, combinatorics, graph theory, computability theory and others.

• Primes of special form, such as prime k-tuple
• The abc conjecture
• Numbers with special property involving divisors, such as perfect numbers
• Residual orders and Discrete logarithms modulo a prime or a prime power
• Integer sequences with special additive property, such as Sidon sets
• Combinatorial Design
• Ramsey Theory
• Cardinals
• Computational property of number theoretic algorithms and combinatorial algorithms

At present, my research interest lies in properties of values of classical arithmetic functions related to divisors of integers, such as σ and φ.

Course (2017)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/25) Report Problems tex (in Japanese) pdf (in Japanese)

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/1) Extra exercises tex (in Japanese) pdf (in Japanese) (8/4 revised) tex (in Japanese) pdf (in Japanese) Figures (zip)

Course (2016)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)

Course (2015)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Linear mappings between vector spaces tex (in Japanese) pdf (in Japanese)

(7/17) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

(7/17) Sums and intersections of vector spaces tex (in Japanese) pdf (in Japanese)

(6/30) Vector spaces tex (in Japanese) pdf (in Japanese) (Addendum) tex (in Japanese) pdf (in Japanese)

(6/6) Report Problems tex (in Japanese) pdf (in Japanese)

(6/5) Linear transformations in plane and space tex (in Japanese) pdf (in Japanese)

(5/29) Vectors in plane and space tex (in Japanese) pdf (in Japanese)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/20) Outline of answers of the examination problems tex (in Japanese) pdf (in Japanese)

Course (2014)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Oct.-Feb. / Fri / 12:50-14:20)

(1/18) Calculation of fractions tex (in Japanese) pdf (in Japanese)

See old lecture notes for calculation of natural numbers.

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(7/29) The 5-6th lectures tex (in Japanese) pdf (in Japanese)

(7/29) The 4-5th lectures tex (in Japanese) pdf (in Japanese)

(7/22) The third-4th lectures tex (in Japanese) pdf (in Japanese)

(5/27) The second-third lectures tex (in Japanese) pdf (in Japanese)

• Set theoretical definition of addition of natural numbers, the associative law and the commutative law involving multi-terms and a problem concerning to palindromic numbers are added

(5/13) The first-second lectures tex (Unicode, in Japanese) pdf (in Japanese)

• Set theoretical definition of natural numbers is added

Course (2013)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(5/7) The first lecture tex (Unicode, in Japanese) pdf (in Japanese)

(5/20) The second-third lecture tex (in Japanese) pdf

Course (2011)

Kyoto Univ. / Basic Mathematics IA (Fri / 8:45-10:15, 10:30-12:00)

The examination was held in July 29. It mainly concerns to convergence and limit of sequences and differentiation of functions.

Here is the homework given in Jul 8, Deadline Apr 5. It concerns to differentiation, integration and convergence of series. It is not obligatory.

Here is the homework given in May 20, Deadline July 1. It mainly concerns to convergence of real sequences. It is not obligatory.

Course (2010)

Kyoto Univ. / Linear Algebra B (Wed / 10:30-12:00)

The examination was held in January 26. It mainly concerns to linear mappings between vector spaces, the method of least squares and the eigenvalue problem.

A quiz was held in December 8. It mainly concerns to linear independence of vectors.

Publications

1. Odd perfect numbers of a special form, Colloq. Math. 103 (2005), 303--307. dvi tex
2. Unitary super perfect numbers, Math. Pannon. 19 (2008), 37--47. dvi tex
3. Linear equations involving iterates of $\sigma(N)$, INTEGERS 9 supplement A15. dvi tex
4. On diophantine equations $x^m=y^{n_1}+y^{n_2}+\ldots +y^{n_k}$, Glasgow Math. J. 51 (2009), 143--148. dvi tex
5. On the simoultaneous equations $\sigma(2^a)=p^{f_1}q^{g_1}, \sigma(3^b)=p^{f_2}q^{g_2}, \sigma(5^c)=p^{f_3}q^{g_3}$, Publ. Math. Debrecen 93 (2018), 57--71, the preprint version in arXiv.
6. Infinitary superperfect numbers Ann. Math. Inform. 47 (2017), 211--218, see the journal's website.
7. On equations $\sigma(n)=\sigma(n+k)$ and $\varphi(n)=\varphi(n+k)$, J. Combin. Number Theory 9 (2017), 15--21, the author's final version in arXiv.
8. 2 and 9 are the only biunitary superperfect numbers, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 247--256, see the journal's website.

Talks

An exponential diophantine equation related to odd perfect numbers (at Diophantine Analysis and Related Fields 2018) pdf (3/4/2018) source (3/4/2018)

Three-term Machin-type formulae (at RIMS Workshop 2018 "Analytic Number Theory and Related Topics" , 10/29/2018) (11/12/2018) (pdf) source (zip)