(in Japanese)

About me

I am 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, GCOE-PD at Department of Mathematics at Kyoto University
2010/10, Part-time teacher (Additional)

Address: 606-8502, Kitashirakawaoiwakecho, Sakyo-ku, Kyoto city, Kyoto, Japan.

Department of Mathematics,
Graduate School of Science,
Kyoto University

e-mail: tyamada at math.kyoto-u.ac.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 (2011)

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.

• Problems in the examination held in July 29, 8:45-10:15 (in Japanese) Answers (in Japanese)
• Problems in the examination held in July 29, 10:30-12:00 (in Japanese) Answers (in Japanese)
• Problems in the supplementary examination (in Japanese) Answers (in Japanese)

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

• Homework in Jul 8 (in Japanese)

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

• Homework in May 20 (in Japanese)
• On the supremum of a set (related to homework in May 20) (7/6)
• Solutions of homework in May 20 (7/6)

Course (2010)

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.

• Problems and solutions of the quiz held in January 26 (in Japanese)

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

• Problems and solutions of the quiz held in December 8 (in Japanese)

Documents

Proofs of the infinitude of primes (1/12/2010) TeX source(1/12/2010)

Publications

1. Odd perfect numbers of a special form, Colloq. Math. 103 (2005), 303--307. dvi tex pdf
2. Unitary super perfect numbers, Math. Pannon. 19 (2008), 37--47. dvi tex pdf
3. Linear equations involving iterates of $\sigma(N)$, INTEGERS 9 supplement A15. dvi tex pdf
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 pdf

Links

Number Theory Web

Number Theory List