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Masanobu KANEKO Last modified date：2021.04.07

Professor / Department of Mathematics
Faculty of Mathematics


Graduate School
Department of Mathematics
Graduate School of Mathematics
Undergraduate School
Department of Mathematics
School of Sciences


Homepage
https://kyushu-u.pure.elsevier.com/en/persons/masanobu-kaneko
　Reseacher Profiling Tool　Kyushu University Pure
http://www2.math.kyushu-u.ac.jp/~mkaneko/
Masanobu Kaneko .
Academic Degree
Doctor of Science
Country of degree conferring institution (Overseas)
No
Field of Specialization
Number Theory
Total Priod of education and research career in the foreign country
02years06months
Outline Activities
My research field is number theory. My recent subjects of study are multiple zeta values and related functions, finite multiple zeta values, and the behavior at real quadratics of the elliptic modular function.

I am supervising master and doctoral students based on these studies.

I am a member of the committee of algebra section of the mathematical society of Japan.

I am the editor-in-chief of the Kyushu Journal of Mathematics, and an editor of three other international mathematical journals.
Research
Research Interests
  • modular form, quasimodular form, elliptic modular function
    keyword : modular form, elliptic modular function
    1990.09Modular and quasimodular forms.
  • multiple zeta values, poly-Bernoulli numbers
    keyword : multiple zeta value, poly-Bernoulli number
    1995.07Study of multiple zeta values. Use regularizations, derivations in an algebraic setting, etc..
Academic Activities
Books
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Papers
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1. Y. Ihara, M. Kaneko, A. Yukinari, On some properties of the universal power series for Jacobi sums, Advanced Studies in Pure Math., 12, 65-86, 1987.06.
2. M. Kaneko, A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders, Proc. of Japan Acad., 66A, 7, 201-203, 1990.06.
3. M. Kaneko, D. Zagier, A generalized Jacobi theta function and quasimodular forms , Progress in Math., 129, 165-172, 1995.06.
4. M. Kaneko, A Recurrence Formula for the Bernoulli Numbers, Proc. of Japan Acad., 71A, 8, 192-193, 1995.06.
5. M. Kaneko, Poly-Bernoulli numbers, J. de Theorie des Nombres de Bordeaux, 9, 199-206, 1997.04.
6. T. Asai, M. Kaneko, H. Ninomiya, Zeros of certain modular functions and an application, Comment. Math. Univ. St. Pauli, 46, 1, 93-101, 1997.04.
7. Masanobu Kaneko, Don Zagier, Supersingular j-invariants, hypergeometric series, and Atkin's
orthogonal polynomials, AMS/IP Studies in Advanced Mathematics, vol. 7, 97--126., 1998.04.
8. Masanobu Kaneko, On the zeros of certain modular forms, Number Theory and its Applications, 2, 193-197, 193--197., 1999.04.
9. Masanobu Kaneko, Traces of singular moduli and the Fourier
coefficients of the elliptic modular function $j(\tau)$, CRM Proceedings and Lecture Notes, vol. 19, 173--176., 1999.04.
10. Masanobu Kaneko, Nobushige Kurokawa, Masato Wakayama, A variation of Euler's approach to values of the Riemann zeta function, Kyushu J. Math., vol. 57-1, 175--192, 2003.03.
11. Masanobu Kaneko, Masao Koike, On modular forms arising from a differential
equation of hypergeometric type, The Ramanujan J., 10.1023/A:1026291027692, 7, 1-3, 145-164, vol. 7, 145--164., 2003.09.
12. K. Ihara, M. Kaneko and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compositio Math., vol. 142-02, 307--338, 2006.04.
13. H. Gangl , M. Kaneko and D. Zagier, Double zeta values and modular forms, Proceedings of the conference in memory of Tsuneo Arakawa, 71--106, 2006.07.
14. M. Kaneko and M. Koike, On extremal quasimodular forms, Kyushu J. Math., vol. 60-2, 457--470, 2006.09.
15. Masanobu KANEKO, Yuichi SAKAI, The Ramanujan-Serre differential operators and certain elliptic curves, Proc. Amer. Math. Soc., 141, 3421-3429, 2013.01.
16. Masanobu KANEKO, Kiyokazu NAGATOMO, Yuichi SAKAI, Modular forms and second order differential equations — applications to vertex operator algebras, Letters in Mathematical Physics, 103, 4, 439-453, 2013.04.
17. Masanobu KANEKO, Kohtaro IMATOMI, Erika TAKEDA, Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values, Journal of Integer Sequences, 17, 14.4.5, 2014.02.
18. M. Kaneko, K. Nagatomo, and Y. Sakai, The third order modular linear differential equations, Journal of Algebra, 485, 1, 332-352, 2017.02.
19. Masanobu Kaneko, Shuji Yamamoto, A new integral–series identity of multiple zeta values and regularizations, Selecta Mathematica, New Series, 10.1007/s00029-018-0400-8, 24, 3, 2499-2521, 2018.07, We present a new “integral = series” type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over Q. We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima’s relation is discussed as well..
20. Masanobu Kaneko, Hirofumi Tsumura, Zeta functions connecting multiple zeta values and poly-Bernoulli numbers, Adv. Stud. Pure Math, 84, 181-204, 2020.03.
Presentations
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Membership in Academic Society
  • American Mathematical Society
Awards
  • Research on quasimodular forms and multiple zeta values
Educational
Educational Activities
I am supervising several master and doctoral students. The goal is to make them write up their own research papers as master or doctoral theses.
Sometimes I give lectures at other universities in number theory at various levels.
Social
Professional and Outreach Activities
Voluntary lectures at several high schools in Fukuoka, Saga, and Nagasaki..


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