Shingo Saito | Last modified date：2022.06.25 |

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Academic Degree

PhD in Mathematics, University of London

Country of degree conferring institution (Overseas)

Yes

Field of Specialization

Mathematics

Outline Activities

- Research

My research interests range from classical real analysis and multiple zeta values in pure mathematics to actuarial science in applied mathematics.

Classical real analysis deals with problems closely related to counterexamples occasionally given in a first course in real analysis. For example, it is rather easy to construct a function that is continuous on the irrationals and discontinuous on the rationals, whereas there does not exist a function that is continuous on the rationals and discontinuous on the irrationals. I mainly use intricate epsilon-delta arguments to address problems in this area, but sometimes need some knowledge of descriptive set theory, which studies the complexity of sets and functions.

Multiple zeta values are a multivariate generalization of Riemann zeta values and have appeared in many different areas including knot theory and mathematical physics. I employ analytic and combinatorial methods to study the relations that exist in large numbers among the values.

I also work on various practical problems in general insurance in collaboration with an insurance company, applying probabilistic and statistical techniques to suitably constructed mathematical models.

- Teaching

Being a member of the Faculty of Arts and Science, I am involved in a number of courses aimed mainly at first-year undergraduate students.

I also teach actuarial science to postgraduate students at the Graduate School of Mathematics.

My research interests range from classical real analysis and multiple zeta values in pure mathematics to actuarial science in applied mathematics.

Classical real analysis deals with problems closely related to counterexamples occasionally given in a first course in real analysis. For example, it is rather easy to construct a function that is continuous on the irrationals and discontinuous on the rationals, whereas there does not exist a function that is continuous on the rationals and discontinuous on the irrationals. I mainly use intricate epsilon-delta arguments to address problems in this area, but sometimes need some knowledge of descriptive set theory, which studies the complexity of sets and functions.

Multiple zeta values are a multivariate generalization of Riemann zeta values and have appeared in many different areas including knot theory and mathematical physics. I employ analytic and combinatorial methods to study the relations that exist in large numbers among the values.

I also work on various practical problems in general insurance in collaboration with an insurance company, applying probabilistic and statistical techniques to suitably constructed mathematical models.

- Teaching

Being a member of the Faculty of Arts and Science, I am involved in a number of courses aimed mainly at first-year undergraduate students.

I also teach actuarial science to postgraduate students at the Graduate School of Mathematics.

Research

**Research Interests**

- classical real analysis

keyword : typical functions

2004.09. - multiple zeta values

keyword : multiple zeta values

2009.01. - actuarial science

keyword : non-life insurance mathematics

2008.04.

**Academic Activities**

**Papers**

1. | Minoru Hirose, Kohtaro Imatomi, Hideki Murahara, and Shingo Saito, Ohno-type relations for classical and finite multiple zeta-star values, Kyushu Journal of Mathematics, 10.2206/kyushujm.75.115, 75, 1, 115-124, 2021.02, [URL]. |

2. | Minoru Hirose, Hideki Murahara, and Shingo Saito, Polynomial generalization of the regularization theorem for multiple zeta values, Publications of the Research Institute for Mathematical Science, 10.4171/PRIMS/56-1-9, 56, 1, 207-215, 2020.01, [URL]. |

3. | Hideki Murahara and Shingo Saito, Restricted sum formula for finite and symmetric multiple zeta values, Pacific Journal of Mathematics, 10.2140/pjm.2019.303.325, 303, 1, 325-335, 2019.12, [URL]. |

4. | Minoru Hirose, Hideki Murahara, and Shingo Saito, Weighted sum formula for multiple harmonic sums modulo primes, Proceedings of the American Mathematical Society, 10.1090/proc/14588, 147, 8, 3357-3366, 2019.08, [URL]. |

5. | Masanobu Kaneko, Kojiro Oyama, Shingo Saito, Analogues of the Aoki-Ohno and Le-Murakami relations for finite multiple zeta values, Bulletin of the Australian Mathematical Society, 10.1017/S0004972718001260, 100, 1, 34-40, 2019.07, [URL]. |

6. | Shingo Saito, Noriko Wakabayashi, Bowman-Bradley type theorem for finite multiple zeta values, Tohoku Mathematical Journal, 10.2748/tmj/1466172771, 68, 2, 241-251, 2016.06, [URL]. |

7. | Shingo Saito, Noriko Wakabayashi, Sum formula for finite multiple zeta values, Journal of the Mathematical Society of Japan, 10.2969/jmsj/06731069, 67, 3, 1069-1076, 2015.07, [URL]. |

8. | David Preiss, Shingo Saito, Knot points of typical continuous functions, Transactions of the American Mathematical Society, 10.1090/S0002-9947-2013-06100-4, 366, 2, 833-856, 2014.02, [URL]. |

9. | Hiroki Kondo, Shingo Saito, Tatsushi Tanaka, The Bowman-Bradley theorem for multiple zeta-star values, Journal of Number Theory, 10.1016/j.jnt.2012.03.012, 132, 9, 1984-2002, [URL]. |

10. | Shingo Saito, Tatsushi Tanaka, Noriko Wakabayashi, Combinatorial remarks on the cyclic sum formula for multiple zeta values, Journal of Integer Sequences, 14, Article 11.2.4, [URL]. |

**Membership in Academic Society**

- Mathematical Society of Japan
- Institute of Actuaries of Japan
- Japanese Association of Risk, Insurance and Pensions

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