Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Masanobu KANEKO Last modified date:2023.05.30

Professor / Division of Algebra and Geometry / Faculty of Mathematics

1. Masanobu Kaneko, Takuya Murakami, Amane Yoshihara, On finite multiple zeta values of level two, Pure and Applied Mathematics Quarterly, 19, 1, 267-280, 2023.02.
2. Masanobu Kaneko, Akihito Ebisu, Yoshishige Haraoka, Hiroyuki Ochiai, Takeshi Sasaki, Masaaki Yoshida, A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions, Osaka Journal of Mathematics, 60, 1, 153-206, 2023.01.
3. Masanobu Kaneko, Daniel Duverney, Carsten Elsner, Youhei Tachiya, A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers, Reseach in Number Theory, 8, 2, Paper No. 31, 13 pp,, 2022.03.
4. Masanobu Kaneko, Takuya Murakami, Hideki Murahara, Quasi-derivation relations for multiple zeta values revisited, Abh. Math. Semin. Univ. Hamburg, 90, 151-160, 2021.02.
5. Masanobu Kaneko, Yoshinori Mizuno, Genus character L-functions of quadratic orders and class numbers, Journal of the London Mathematical Society, 10.1112/jlms.12313, 102, 1, 69-98, 2020.08, An explicit form of genus character (Formula presented.) -functions of quadratic orders is presented in full generality. As an application, we generalize a formula due to Hirzebruch and Zagier on the class number of imaginary quadratic fields expressed in term of the continued fraction expansion..
6. Masanobu Kaneko, Maneka Pallewatta, Hirofumi Tsumura, On poly-cosecant numbers, J. of Integer Sequences, 23, Article 20.6.4, 12pp, 2020.06.
7. Masanobu Kaneko, Hirofumi Tsumura, Zeta functions connecting multiple zeta values and poly-Bernoulli numbers, Adv. Stud. Pure Math, 84, 181-204, 2020.03.
8. Carsten Elsner, Masanobu Kaneko, Yohei Tachiya, Algebraic independence results for the values of the theta-constants and some identities, Journal of the Ramanujan Mathematical Society, 35, 1, 71-80, 2020.03, In the present work, we give algebraic independence results for the values of the classical theta-constants ϑ2(τ), ϑ3(τ), and ϑ4(τ). For example, the two values ϑα(mτ) and ϑβ(nτ) are algebraically independent over Q for any τ in the upper half-plane when eπiτ is an algebraic number, where m, n ≥ 1 are integers and α, β ∈ {2, 3, 4} with (m, α) ≠ (n, β). This algebraic independence result provides new examples of transcendental numbers through some identities found by S. Ramanujan. We additionally give some explicit identities among the three theta-constants in particular cases..
9. 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, 2019.08, We establish finite analogues of the identities known as the Aoki-Ohno relation and the Le-Murakami relation in the theory of multiple zeta values. We use an explicit form of a generating series given by Aoki and Ohno..
10. Masanobu Kaneko, An introduction to classical and finite multiple zeta values, Publications Mathematiques de Besancon, 2019.08.
11. Masanobu Kaneko, Hirofumi Tsumura, MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS, Nagoya Mathematical Journal, 10.1017/nmj.2017.16, 232, 19-54, 2018.12, We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the ξ-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions..
12. 金子昌信, 山本修司, 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.
13. M. Kaneko and M. Yoshida, Point-arrangements in the real projective spaces and the Fibonacci polynomials, Kumamoto Journal of Mathematics, 31, 1-13, 2018.04.
14. Masanobu Kaneko, Fumi Sakurai, Hirofumi Tsumura, On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application, Journal de Theorie des Nombres de Bordeaux, 10.5802/jtnb.1023, 30, 1, 203-218, 2018.01, We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is apparent. Secondly we give an analytic proof of the duality from the viewpoint of our previous study of zeta functions of Arakawa–Kaneko type. As an application, we give a formula that relates poly-Bernoulli numbers to the Genocchi numbers..
15. Masanobu Kaneko, Kiyokazu Nagatomo, Yuichi Sakai, The third order modular linear differential equations, JOURNAL OF ALGEBRA, 10.1016/j.jalgebra.2017.05.007, 485, 332-352, 2017.09, We propose a third order generalization of the Kaneko-Zagier modular differential equation, which has two parameters. We describe modular and quasimodular solutions of integral weight in the case where one of the exponents at infinity is a multiple root of the indicial equation. We also classify solutions of "character type", which are the ones that are expected to relate to characters of simple modules of vertex operator algebras and one-point functions of two-dimensional conformal field theories. Several connections to generalized hypergeometric series are also discussed. (C) 2017 Elsevier Inc. All rights reserved..
16. M. Kaneko, K. Nagatomo, and Y. Sakai, The third order modular linear differential equations, Journal of Algebra, 485, 1, 332-352, 2017.02.
17. M. Kaneko, H. Sakata, and M. Takeuchi, On the parity of calibers of real quadratic orders, Siauliai Mathematical Seminar, 11, 35-43, 2016.09.
18. Yusuke Arike, Masanobu Kaneko, Kiyokazu Nagatomo, Yuichi Sakai, Affine Vertex Operator Algebras and Modular Linear Differential Equations, LETTERS IN MATHEMATICAL PHYSICS, 10.1007/s11005-016-0837-7, 106, 5, 693-718, 2016.05, In this paper, we list all affine vertex operator algebras of positive integral levels whose dimensions of spaces of characters are at most 5 and show that a basis of the space of characters of each affine vertex operator algebra in the list gives a fundamental system of solutions of a modular linear differential equation. Further, we determine the dimensions of the spaces of characters of affine vertex operator algebras whose numbers of inequivalent simple modules are not exceeding 20..
19. Masanobu Kaneko, Mika Sakata, ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 10.1017/S0004972715001227, 93, 2, 186-193, 2016.04, We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height..
20. 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.
21. Kohtaro Imatomi, Masanobu Kaneko, Erika Takeda, Multi-poly-bernoulli numbers and finite multiple zeta values, Journal of Integer Sequences, 17, 4, 1-12, 2014.02, We define the multi-poly-Bernoulli numbers slightly differently from the similar numbers given in earlier papers by Bayad, Hamahata, and Masubuchi, and study their basic properties. Our motivation for the new definition is the connection to “finite multiple zeta values”, which have been studied by Hoffman and Zhao, among others, and are recast in a recent work by Zagier and the second author. We write the finite multiple zeta value in terms of our new multi-poly-Bernoulli numbers..
22. Masanobu Kaneko, Koji Tasaka, Double zeta values, double Eisenstein series, and modular forms of level 2, MATHEMATISCHE ANNALEN, 10.1007/s00208-013-0930-5, 357, 3, 1091-1118, 2013.11, We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms of level 2..
23. Kaneko Masanobu, Sakai Yuichi, THE RAMANUJAN-SERRE DIFFERENTIAL OPERATORS AND CERTAIN ELLIPTIC CURVES, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 10.1090/S0002-9939-2013-11917-9, 141, 10, 3421-3429, 2013.10, For several congruence subgroups of low levels and their conjugates, we derive differential equations satisfied by the Eisenstein series of weight 4 and relate them to elliptic curves, whose associated new forms of weight 2 constitute the list of Martin and Ono of new forms given by eta-products/quotients..
24. Kaneko Masanobu, Nagatomo Kiyokazu, Sakai Yuichi, Modular Forms and Second Order Ordinary Differential Equations: Applications to Vertex Operator Algebras, LETTERS IN MATHEMATICAL PHYSICS, 10.1007/s11005-012-0602-5, 103, 4, 439-453, 2013.04, We study the relation between the Kaneko–Zagier equation and the Mathur–Mukhi–Sen classification, and extend it to the case of solutions with logarithmic terms, which correspond to pseudo-characters of non-rational vertex operator algebras. As an application, we prove a non-existence theorem of rational vertex operator algebras..
25. Yutaro Honda, Masanobu Kaneko, ON FOURIER COEFFICIENTS OF SOME MEROMORPHIC MODULAR FORMS, BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 10.4134/BKMS.2012.49.6.1349, 49, 6, 1349-1357, 2012.11, We prove a congruence modulo a prime of Fourier coefficients of several meromorphic modular forms of low weights. We prove the result by establishing a generalization of a theorem of Garthwaite..
26. Masanobu Kaneko and Keita Mori, Congruences modulo 4 of calibers of real quadratic fields, Ann. Sci. Math. Quebec, 35, 2, 185--195, 2011.12.
27. Hiroshi Yoshida, Yoshihiro Miwa, Masanobu Kaneko, Elliptic curves and Fibonacci numbers arising from Lindenmayer system with symbolic computation, APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 10.1007/s00200-011-0143-7, 22, 2, 147-164, 2011.03, Starting from an egg, the multicell becomes a set of cells comprising a variety of types to serve functions. This phenomenon brings us a bio-motivated Lindenmayer system. To investigate conditions for a variety of cell types, we have constructed a stochastic model over Lindenmayer systems. This model considers interactive behaviors among cells, yielding complicated polynomials. Using symbolic computation, we have derived explicit relations between cell-type diversity and cell-type ratio constraint. These relations exhibit elliptic curve-and Fibonacci number-related patterns. This is the first example of elliptic curves to appear in the Lindenmayer context. A survey of the rational points and the quadratic irrational numbers on the derived curves has revealed Fibonacci-related periodic and quasiperiodic patterns. Further we have found that in some region, there are only two elliptic curve-related periodic patterns..
28. Masanobu Kaneko, Yasuo Ohno, On a kind of duality of multiple zeta-star values, International Journal of Number Theory, 10.1142/S179304211000385X, 6, 8, 1927-1932, 2010.12, A duality-type relation for height one multiple zeta-star values is established. A conjectural generalization to the case of arbitrary height is also presented..
29. Masanobu Kaneko, Poly-Bernoulli numbers and related zeta functions, MSJ Memoir, 21, 73--85, 2010.02.
30. KANEKO Masanobu, OBSERVATIONS ON THE 'VALUES' OF THE ELLIPTIC MODULAR FUNCTION j(τ) AT REAL QUADRATICS, Kyushu Journal of Mathematics, 10.2206/kyushujm.63.353, 63, 2, 353-364, 2009.10, We define 'values' of the elliptic modular j-function at real quadratic irrationalities by using Hecke's hyperbolic Fourier expansions, and present some observations based on numerical experiments..
31. KAJIWARA Kenji, KANEKO Masanobu, NOBE Atsushi, TSUDA Teruhisa, Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve, Kyushu Journal of Mathematics, 10.2206/kyushujm.63.315, 63, 2, 315-338, 2009.10, We present a solvable two-dimensional piecewise linear chaotic map that arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the map is derived by the ultradiscretization of the duplication map associated with the Hesse cubic curve. We also show that it is possible to obtain the non-trivial ultradiscrete limit of the solution in spite of a problem known as 'the minus-sign problem.' © 2009 Faculty of Mathematics, Kyushu University..
32. M. Kaneko, M.Noro and K.Tsurumaki, On a conjecture for the dimension of the space of the multiple zeta values, Software for Algebraic Geometry, IMA 148, 47--58., 2008.04.
33. M.Kaneko, A note on poly-Bernoulli numbers and multiple zeta values, Diophantine analysis and related fields (DARF 2007/2008), AIP Conf. Proc. 976, 118--124, 2008.03.
34. M. Kaneko, On an extension of the derivation relation for multiple zeta values, The Conference on $L$-functions, (L. Weng and M. Kaneko eds.), 89--94, 2007.01.
35. M. Chida and M. Kaneko, On ordinary primes for modular forms and the theta operator, Proc. Amer. Math. Soc., 135, 1001--1005, 2007.01.
36. Masanobu Kaneko, Naruya Niiho, On some properties of polynomials related to hypergeometric modular forms, RAMANUJAN JOURNAL, 10.1007/s11139-006-0146-3, 12, 3, 321-325, 12-3, 321--325., 2006.12, We find the discriminants, Galois groups, and prove the irreducibility of certain hypergeometric polynomials, which are closely related to modular forms and supersingular elliptic curves..
37. Masanobu Kaneko, On modular forms of weight (6n + l)/5 satisfying a certain differential equation, NUMBER THEORY, 97-102, 2006.12, We study solutions of a differential equation which arose in our previous study of supersingular elliptic curves. By choosing one fifth of an integer k as the parameter involved in the differential equation, we obtain modular forms of weight k as solutions. It is observed that this solution is also related to supersingular elliptic curves..
38. Masanobu Kaneko, Masao Koike, On extremal quasimodular forms, KYUSHU JOURNAL OF MATHEMATICS, 60, 2, 457-470, vol. 60-2, 457--470, 2006.09, We define and study 'extremal' quasimodular forms. Some explicit descriptions of such forms are given. Connections with certain differential equations and Atkin's orthogonal polynomials, and the positivity of the Fourier coefficients, are also discussed..
39. 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.
40. 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.
41. M. Kaneko, On the local factor of the zeta function of quadratic orders, Zeta functions, Topology, and Quantum Physics, Developments in Mathematics, 14, 75-79, Vol.14, 75--79, 2005.04.
42. Arakawa Tsuneo, Kaneko Masanobu, On multiple L-values, Journal of the Mathematical Society of Japan, 10.2969/jmsj/1190905444, 56, 4, 967-991, vol. 56-4, 967--991, 2004.04, We formulate and prove reguralized double shuffle and derivation relations for multiple L-values. A description of principal part of a multiple L-function is also given..
43. Masanobu Kaneko, Masaaki Yoshida, The kappa function, Int. J. Math., 10.1142/S0129167X0300206X, 14, 9, 1003-1013, vol. 14-9, 1003--1013, 2003.12.
44. Kaneko Masanobu, Koike Masao, On Modular Forms Arising from a Differential Equation of Hypergeometric Type, The Ramanujan Journal, 10.1023/A:1026291027692, 7, 1-3, 145-164, vol. 7, 145--164., 2003.09, Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed..
45. Masanobu Kaneko, Masao Koike, Quasimodular forms as solutions to a differential equation of hypergeometric type, Galois Theory and Modular Forms, 329--336, 2003.07.
46. Masanobu Kaneko, Hiroyuki Ochiai, On coefficients of Yablonskii-Vorob'ev polynomials, J. Math. Soc. Japan, 10.2969/jmsj/1191418760, 55, 4, 985-993, vol. 55-4, 985--993, 2003.04.
47. 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.
48. KANEKO Masanobu, KUROKAWA Nobushige, WAKAYAMA Masato, A VARIATION OF EULER′S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION, Kyushu Journal of Mathematics, 10.2206/kyushujm.57.175, 57, 1, 175-192, 2003.02.
49. Kaneko Masanobu, Tachibana Katsuichi, When is a polygonal pyramid number again polygonal?, Rocky Mountain Journal of Mathematics, 10.1216/rmjm/1030539614, 32, 1, 149-165, vol. 32-1, 149--165., 2002.04, We consider a Diophantine equation arising from a generalization of the classical Lucas problem of the square pyramid: when is the sum of the first m-gonal numbers n-gonal? We use the theory of elliptic surfaces to deduce several families of parametric solutions of the problem..
50. Masanobu Kaneko, Naoya Todaka, Hypergeometric modular forms and supersingular elliptic curves, Proceedings on Moonshine and related topics, CRM Proceedings and Lecture Notes, vol. 30, 79--83., 2002.04.
51. Masanobu Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, Journal of Integer Sequences, 3, 2, 1-7, 2000.12, A direct proof is given for Akiyama and Tanigawa'a algorithm for computing Bernoulli numbers. The proof uses a closed formula for Bernoulli numbers expressed in terms of Stirling numbers. The outcome of the same algorithm with di erent initial values is also brie y discussed..
52. Masanobu Kaneko, On the zeros of certain modular forms, Number Theory and its Applications, 2, 193-197, 193--197., 1999.04.
53. 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.
54. T Arakawa, M Kaneko, Multiple zeta values, poly-Bernoulli numbers, and related zeta functions, NAGOYA MATHEMATICAL JOURNAL, 153, 189-209, 1999.03, We study the function
and show that the poly-Bernoulli numbers introduced in our previous paper are expressed as special values at negative arguments of certain combinations of these functions. As a consequence of our study, we obtain a series of relations among multiple zeta values..
55. Keiji Horiuchi, Yuichi Futa, Ryuichi Sakai, Masanobu Kaneko, Masao Kasahara, 素数位数を有する楕円曲線の構成とその計算量評価, 電気情報通信学会論文誌A, J82-A, 8, 1269-1277, 1999, 楕円暗号において,楕円曲線の群の位数は重要なパラメータである.特に,その位数が素数であ
56. 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.
57. M. Kaneko, Poly-Bernoulli numbers, J. de Theorie des Nombres de Bordeaux, 9, 199-206, 1997.04.
58. 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.
59. M Kaneko, On Ito's observation on coefficients of the modular polynomial, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 72, 5, 95-96, 1996.05.
60. Masanobu Kaneko, The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Memoirs of the Faculty of Engineering and Design, 1-5, 1996.03.
61. M. Kaneko, D. Zagier, A generalized Jacobi theta function and quasimodular forms, Progress in Math., 129, 165-172, 1995.06.
62. M. Kaneko, A Recurrence Formula for the Bernoulli Numbers, Proc. of Japan Acad., 71A, 8, 192-193, 1995.06.
63. T ODAGAKI, M KANEKO, SELF-SIMILARITY OF BINARY QUASI-PERIODIC SEQUENCES, JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 10.1088/0305-4470/27/5/030, 27, 5, 1683-1690, 1994.03, Self-similarity in binary quasiperiodic sequences generated by a projection method is shown to exist when and only when it is associated with quadratic irrational numbers and the explicit self-similarity transformation for an arbitrary quadratic number is obtained. The self-similarity transformation is shown not to be reducible to the simplest form for a class of quadratic numbers..
65. Kaneko Masanobu, Odagaki Takashi, Selfsimilarity in a Class of Quadratic-Quasiperiodic Chains, Journal of the Physical Society of Japan, 10.1143/JPSJ.62.1147, 62, 4, 1147-1152, 1993.01, We prove that quasiperiodic chains associated with a class of quadratic irrational numbers have an inflation symmetry and can be generated from a regular chain by a hyperinflation. We devise the explicit method to find the hyperinflation symmetry and discuss the properties of such a class of quasiperiodic sequences..
68. M. Kaneko, Certain automorphism groups of pro-l fundamental groups of punctured Riemann surfaces, J. of Fac. of Sci., Univ. of Tokyo, 36, 363-372, 1989.06.
69. H. Ichimura, M. Kaneko, On the universal power series for Jacobi sums and the Vandiver conjecture, J. of Number Theory, 31, 312-334, 1989.06.
70. M. Asada, M. Kaneko, On the automorphism group of some pro-$ell$ fundamental groups, Advanced Studies in Pure Math., 12, 65-86, 1987.06.
71. 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.