Publications

Preprints

[1]Cid Reyes-Bustos and Masato Wakayama:
Two-photon quantum Rabi models - Spectral degeneracy and symmetries.
Preprint 2026. ArXiv:2609.00750

Papers (Journal papers and Conference Proceedings (*) )

[115] K. Kimoto, M. Wakayama:
Partition functions for non-commutative harmonic oscillators and related divergent series,
Indagationes Mathematicae 36 (2025), 302–336.
DOI: https://doi.org/10.1016/j.indag.2024.05.011

[114] C. Reyes-Bustos, M. Wakayama:
Zeta limits for the spectrum of quantum Rabi models, Journal of Mathematical Physics, 65, 093503 (2024).
DOI: https://doi.org/10.1063/5.0217399

[111] C. Reyes-Bustos and M. Wakayama:
The heat kernel for the quantum Rabi model,
Advances in Theoretical and Mathematical Physics, 5 (2022), 1347-1447.

[110] C. Reyes-Bustos and M. Wakayama:
Degeneracy and hidden symmetry -- an asymmetric quantum Rabi model with an integer bias,
Communications in Number Theory and Physics, 16, 615–672, 2022.

[109] Cid Reyes-Bustos, Daniel Braak and Masato Wakayama:
Remarks on the hidden symmetry of the asymmetric quantum Rabi model, Journal of Physics A: Mathematical and Theoretical, 54 (2021), 285202.

[108] Cid Reyes-Bustos and Masato Wakayama:
Heat kernel for the quantum Rabi model: II. Propagators and spectral determinants, J. Phys. A: Math. Theor. 54（2021),115202

[107] K. Kimoto and M. Wakayama:
Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals,
Annales de l’Institut Henri Poincaré D, 10(2023), 205-275 (December 2022, online first).
DOI: https://doi.org/10.4171/AIHPD/129

[106] K. Kimoto, C. Reyes-Bustos and M. Wakayama:
Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model, International Mathematics Research Notices, Volume 2021, Issue 12, June 2021, Pages 9458–9544

[105] M. Wakayama:
Number theoretic study in quantum interactions, 85-90, “Mathematics, Quantum Theory, and Cryptography”, eds. T. Takagi et al., Springer, 2020.

[104*] C. Reyes-Bustos and M. Wakayama:
Spectral degeneracies in the asymmetric quantum Rabi model, “Mathematical Modelling for Next-Generation Cryptography" eds. T. Takagi, et al., Springer, 2018, 117-137.

[103] M. Wakayama:
Symmetry of asymmetric quantum Rabi models, “Mathematical Modelling for Next-Generation Cryptography" Journal of Physics A: Mathematical and Theoretical, 50, (2017), 174001[20 pages].

[102] J. Faraut and M. Wakayama:
Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials Mathematica Scandinavica, 120, (2017), 87-114.

[101] M. Wakayama:
Equivalence between the eigenvalue problem of non-commutative harmonic oscillators and existence of holomorphic solutions of Heun differential equations, eigenstates degeneration and Rabi model, International Mathematics Research Notices, 2016:145, (2016)

[100] K. Hamamoto, K. Kimoto, K. Tachibana and M. Wakayama:
Wreath determinants for group-subgroup pairs, Journal of Combinatorial Theory, Series A 133, (2015), 76-96.

[99] M. Wakayama and T. Yamasaki:
The quantum Rabi model and Lie algebra representations of sl_2, Journal of Physics A: Mathematical and Theoretical, 47, (2014), 335203 [17 pages]

[98*]M. Wakayama:
Remarks on quantum interaction models by Lie theory and modular forms via non-commutative harmonic oscillators, pp17-34, A Mathematical Approach to Research Problems of Science and Technology-Theoretical Basis and Developments in Mathematical Modeling, Series: Mathematics for Industry, Vol. 5, Nishii, R. (et al.) (Eds.) 2014.

[97*]M. Wakayama:
A Lie theoretic proposal on algorithms for the spherical harmonic lighting, 43-54, Mathematical Progress in Expressive Image Synthesis I-Extended and Selected Results from the Symposium MEIS2013, K. Anjyo (Ed.) 2014.

[96] M. Wakayama:
Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation, Proceedings of the Japan Academy, Volume 89, Number 6 (2013), 69-73.

[95] J. Faraut and M. Wakayama:
Invariant differential operators on the Heisenberg group and Meixner-Pollaczek polynomials, Advances in Pure and Applied Mathematics. Volume 4, Issue 1, Pages 41-66, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: 10.1515/apam-2013-0204, April 2013.

[94] N. Kurokawa, Y. Yamasaki and M. Wakayama:
Milnor-Selberg zeta functions and zeta regularizations, J. Geometry and Physics, Volume 64, 2013, 120-145.

[93] M. Wakayama and K.Yamamoto:
Non-linear algebraic differential equations satisfied by certain family of elliptic functions, The Ramanujan Journal,February 2013, 30 (2), 173-186.

[92*] K. Kimoto, M. Wakayama
Spectrum of non-commutative harmonic oscillators and residual modular forms, Noncommutative Geometry and Physics 3, World Scientific (2012), 237-267.

[91] M. Wakayama and Y. Yamasaki:
Higher regularizations for zeros of cuspidal automorphic L-functions of GL(d), Journal de Théorie des Nombres de Bordeaux, 23, (2011), 751-767.

[90] T. Imai, A. Takaesu and M. Wakayama:
Remarks on geodesics for multivariate normal models, J. Math-for-Industry, (2011B-6), 125-130

[89] K. Kimoto, S. Matsumoto and M. Wakayama:
Alpha-determinant cyclic modules and Jacobi polynomials, Transactions of the American Mathematical Society, 361 (2009), 6447-6473.

[88] N. Kurokawa, Y. Yamasaki and M. Wakayama:
Ruelle’s type L-functions versus determinants of Laplacians for torsion free abelian groups, International Journal of Mathematics, 19(8), (2008), 957-979.

[87] N. Kurokawa and M. Wakayama:
Period deformations and Raabe's formulas for generalized gamma and sine functions, Kyushu Journal of Mathematics, 62, (2008) 171-187.

[86] K. Kimoto and M. Wakayama:
Invariant theory for singular α-determinants, Journal of Combinatorial Theory, Series A, 115, (2008) 1-31 .
- arXiv:math/0603699 [math.RT] [26 pages], 2007

[85] K. Kawagoe, Y. Yamasaki and M. Wakayama:
q-Analogues of the Riemann zeta, the Dirichlet L-functions and a crystal zeta function, Forum Mathematicum, 20, (2008), 1-26.

[84*] K. Kimoto and M. Wakayama:
Elliptic curves arising from the spectral zeta functions for non-commutative harmonic oscillators and Γ０(4)-modular forms, Proceedings of the conference on L-functions, World Scientific (2007), 201-218.

[83] T. Ichinose and M. Wakayama:
On the spectral zeta function for the non-commutative harmonic oscillator, Reports on Mathematical Physics, 59, (2007), 421-432.

[82] K. Kimoto and M. Wakayama:
Quantum α-determinant cyclic modules of Uq(gln), Journal of Algebra, 313, (2007), 922-956.

[81] S. Haran, N. Kurokawa and M. Wakayama:
Jackson-Mellin's transform of modular forms and q-zeta functions, Kyushu Journal of Mathematics, 61, (2007), 551-563.

[80] N. Kurokawa, K. Mimachi and M. Wakayama:
Jackson's integral of the Hurwitz zeta function, Rendiconti del Circolo mathemateco di Palermo, 56, (2007), 43-56.

[79] Y. Hashimoto and M. Wakayama:
Splitting density for lifting about discrete groups, Tohoku Mathematical Journal, 59, (2007), 527-545.

[78] N. Kurokawa, H. Ochiai and M. Wakayama:
Milnor's multiple gamma functions, Journal of the Ramanujan Mathematical Society, 21, (2006) 153-167.

[77] S. Matsumoto and M. Wakayama:
Alpha-determinant cyclic modules of gln(C), Journal of Lie Theory, 16, (2006), 393-405.

[76] K. Kimoto and M. Wakayama:
Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators, Kyushu Journal of Mathematics, 60, (2006), 383-404 (with Kazufumi Kimoto).

[75] Y. Yamasaki and M. Wakayama:
Integral representations of q-analogues of the Hurwitz zeta function, Monatshefte für Mathematik, 149, (2006), 141-154.

[74] N. Kurokawa and M. Wakayama:
Algebraicity and transcendency of basic special values of Shintani's double sine functions, Proceedings of the Edinburgh Mathematical Society, 49, (2006), 361-366.

[73] M. Ishiakwa and M. Wakayama:
Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities, Journal of Combinatorial Theory, Series A, 113, (2006), 113-155.

[72] N. Kurokawa and M. Wakayama:
A q-logarithmic analogue of Euler's sine integral, Rendiconti del Seminario Matematico della Universita di Padova, 114, (2005), 51-62.

[71] N. Kurokawa and M. Wakayama:
Gamma and sine functions for Lie groups and period integrals, Indagationes Mathematicae N.S., 16, (2005), 585-607.

[70] Y. Hashimoto and M. Wakayama:
Hierarchy of the Selberg zeta functions, Letters in Mathematical Physics, 73, (2005), 59-70.

[69] N. Kurokawa and M. Wakayama:
Differential algebraicity of multiple sine functions, Letters in Mathematical Physics, 71, (2005), 75-82.

[68] M. Wakayama:
Remarks on Shintani's zeta function, Journal of the Mathematical Sciences, University of Tokyo, 12, (2005), 289-317.

[67] K. Kimoto, N. Kurokawa, S. Matsumoto and M. Wakayama:
Multiple finite Riemann zeta functions, Acta Arithmetica, 116, (2005), 173-187.

[66] T. Ichinose and M. Wakayama:
Special values of the spectral zeta function of the non-commutative harmonic oscillator and confluent Heun equations, Kyushu Journal of Mathematics, 59, (2005), 39-100.

[65] T. Ichinose and M. Wakayama:
Zeta functions for the spectrum of the non-commutative harmonic oscillators, Communications in Mathematical Physics, 258, (2005), 697-739.

[64] N. Kurokawa and M. Wakayama:
Extensions of zeta functions -- examples and a study of the double sine functions, Acta Applicandae Mathematicae, 86, (2005), 179-201.

[63] N. Kurokawa and M. Wakayama:
Regularizations and finite ladders in multiple trigonometry, Journal of the Mathematical Society of Japan, 57, (2005), 1197-1216.

[62] N. Kurokawa and M. Wakayama:
Generalized zeta regularizations, quantum class number formulas, and Appell's O-functions, The Ramanujan Journal, 10, (2005), 291-303.

[61] N. Kurokawa and M. Wakayama:
Certain families of elliptic functions defined by q-series, The Ramanujan Journal, 10, (2005), 23-41.

[60] N. Kurokawa and M. Wakayama:
Zeta functions of q-perfect numbers, Rendiconti del Circolo Matematico di Palermo, 53, (2004), 381-389.

[59] N. Kurokawa and M. Wakayama:
Zeta regularizations, Acta Applicandae Mathematicae, 81, (2004), 147-166.

[58] N. Kurokawa and M. Wakayama:
Ruelle type zeta functions for tori and arithmetics, International Journal of Mathematics, 15, (2004), 691-715.

[57] N. Kurokawa and M. Wakayama:
Absolute tensor products, International Mathematics Research Notices, 2004:5, (2004), 249-260.

[56] N. Kurokawa and M. Wakayama:
Zeta regularized products for multiple trigonometric functions, Tokyo Journal of Mathematics, 27, (2004), 469-480.

[55] N. Kurokawa and M. Wakayama:
Extremal values of multiple trigonometric functions, Kyushu Journal of Mathematics, 58, (2004), 141-166.

[54] K. Kimoto and M. Wakayama:
Remarks on zeta regularized products, International Mathematics Research Notices, 2004:17, (2004), 855-875.

[53] K. Kimoto, N. Kurokawa, C. Sonoki and M. Wakayama:
Some examples of generalized zeta regularized products, Kodai Mathematical Journal, 27, (2004), 321-335.

[52] N. Kurokawa and M. Wakayama:
A note on spectral zeta functions of quantum groups, International Journal of Mathematics, 15, (2004), 125-133.

[51] N. Kurokawa and M. Wakayama:
On q-analogues of the Euler constant and Lerch's limit formula, Proceedings of the American Mathematical Society, 132, (2004), 935-943.

[50] Y. Hashimoto, Y. Iijima N. Kurokawa and M. Wakayama:
Euler's constants for the Selberg and the Dedekind zeta functions, Bulletin of the Belgian Mathematical Society Simon Stevin, 11, (2004), 493-516.

[49] N. Kurokawa and M. Wakayama:
Higher Selberg zeta functions, Communications in Mathematical Physics, 247, (2004), 447-466.

[48] N. Kurokawa and M. Wakayama:
A generalization of Lerch's formula, Czechoslovak Mathematical Journal, 54, (2004), 949-954.

[47] N. Kurokawa and M. Wakayama:
Analyticity of polylogarithmic Euler products, Rendiconti del Circolo Matematico di Palermo, 52, (2003), 382-388.

[46] N. Kurokawa and M. Wakayama:
On q-basic multiple gamma functions, International Journal of Mathematics, 14, (2003), 885-902.

[45] N. Kurokawa and M. Wakayama:
Duplication formulas in triple trigonometry, Proceedings of the Japan Academy, 79, Ser. A (2003), 123-127.

[44] M. Hirano, N. Kurokawa and M. Wakayama:
Half zeta functions, Journal of the Ramanujan Mathematical Society, 18, (2003), 195-209.

[43] N. Kurokawa and M. Wakayama:
Cauchy-Schwarz type inequalities for categories, Kyushu Journal of Mathematics, 57, (2003), 325-331.

[42] K. Kimoto, N. Kurokawa, C. Sonoki and M. Wakayama:
Zeta regularizations and q-analogue of ring sine functions, Kyushu Journal of Mathematics, 57, (2003), 197-215.

[41*] N. Kurokawa, H. Ochiai and M. Wakayama:
Absolute derivations and zeta functions, Documenta Mathematica, (Extra Volume Kato) (2003), 565-584.

[40] M. Kaneko, N. Kurokawa and M. Wakayama:
A variation of Euler's approach to values of the Riemann zeta function, Kyushu Journal of Mathematics, 57, (2003), 175-192.

[39] N. Kurokawa and M. Wakayama:
A comparison between the sum over Selberg's zeroes and Riemann's zeroes, Journal of the Ramanujan Mathematical Society, 18, (2003), 221-236 (Corrections, ibid. 18, (2003), 415-416).

[38] Hitodakari Kuroyama (N. Kurokawa and M. Wakayama):
Dirichlet's prime number theorem for modular groups, Kyushu Journal of Mathematics, 56, (2002), 293-297.

[37] A. Parmeggiani and M. Wakayama:
Corrigenda and remarks to "Non-commutative harmonic oscillators I", Forum Mathematicum, 14, (2002), 539-604, Forum Mathematicum, 15, (2003), 955-963.

[36] N. Kurokawa, Eva-Marie Müller-Stüler, H. Ochiai and M. Wakayama:
Kronecker's Jugendtraum and ring sine functions, Journal of the Ramanujan Mathematical Society, 17, (2002), 211-220.

[35] N. Kurokawa, H. Ochiai and M. Wakayama:
Multiple trigonometry and zeta functions, Journal of the Ramanujan Mathematical Society, 17, (2002), 101-113.

[34] N. Kurokawa and M. Wakayama:
Zeta extensions, Proceedings of the Japan Academy, 78, Ser. A (2002), 126-130.

[33] A. Parmeggiani and M. Wakayama:
A Remark on systems of differential equations associated with representations of sl２(R) and their perturbations, Kodai Mathematical Journal, 25 (2002), 254-277.

[32] N. Kurokawa and M. Wakayama:
Casimir effects on Riemann surfaces, Indagationes Mathematicae N.S. (Koninklijke Nederlandse Akademie van Wetenschappen), 13, (2002), 63-75.

[31] K. Nagatou, M-T. Nakao and M. Wakayama:
Verified numerical computations of eigenvalue problems for non-commutative harmonic oscillators, Numerical Functional Analysis and Optimization, 23, (2002), 633-650.

[30] A. Parmeggiani and M. Wakayama:
Non-commutative harmonic oscillators II, Forum Mathematicum, 14, (2002), 669-690.

[29] K. Kimoto and M. Wakayama:
Equidistribution of holonomy restricted to a homology class about closed geodesics, Forum Mathematicum, 14, (2002), 383-403.

[28] K. Kinoshita and M. Wakayama:
Explicit Capelli Identities for skew symmetric matrices, Proceedings of the Edinburgh Mathematical Society, 45, (2002), 449-465.

[27] A. Parmeggiani and M. Wakayama:
Non-commutative harmonic oscillators I, Forum Mathematicum, 14, (2002), 539-604.

[26] N. Kurokawa and M. Wakayama:
On ζ(3), Journal of the Ramanujan Mathematical Society, 16, (2001), 205-214.

[25] A. Parmeggiani and M. Wakayama:
Oscillator representations and systems of ordinary differential equations, Proceedings of the National Academy of Sciences of the United States of America, 98, (2001), 26-30.

[24] N. Kurokawa, H. Kuroyama and M. Wakayama:
A formula for the multiplicity of the principal series in L２(G/Γ), Forum Mathematicum, 12, (2000), 757-766.

[23] M. Ishikawa and M. Wakayama:
Minor summation formulas of Paffians, Survey and a new identity, Advanced Studies in Pure Mathematics, 28, (Combinatorial Methods in Representation Theory) (2000), 133-142.

[22] M. Ishikawa and M. Wakayama:
Applications of minor summation formulas II, Pfaffians and Schur Polynomials, Journal of Combinatorial Theory, Series A, 88, (1999), 136-157.

[21] P. Sarnak and M. Wakayama:
Equidistribution of holonomy about closed geodesics, Duke Mathematical Journal, 100, (1999), 1-57.

[20] M. Wakayama:
An inequality among infinitesimal characters related to the lowest K-types of discrete series, Proceedings of the Japan Academy, 74,] Ser. A (1998), 57-60.

[19] M. Ishikawa and M. Wakayama:
New Schur function series, Journal of Algebra, 208, (1998), 480-525.

[18] T. Umeda and M. Wakayama:
Another look at the differential operators on the quantum matrix spaces and its applications, Commentarii Mathematici Universitatis Sancti Pauli, 47 Issue 1 (1998) ISSN: 0010-258X, 53-80.

[17] M. Ishikawa, S. Okada and M. Wakayama:
Applications of minor summation formulas I, Littlewood's formulas, Journal of Algebra, 183, (1996), 193-216.

[16] M. Noumi, T. Umeda and M. Wakayama:
Dual pairs, spherical harmonics and a Capelli Identity in quantum group theory, Compositio Mathematica, 104, (1996), 227-277.

[15] M. Ishikawa and M. Wakayama:
Minor summation formula of Pfaffians and Schur functions' identities, Proceedings of the Japan Academy, 71A, (1995), 54-57.

[14] M. Ishikawa and M. Wakayama:
Minor summation formula of Pfaffians, Linear and Multilinear Algebra, 39 (1995), 285-305.

[13] M. Noumi, T. Umeda and M. Wakayama:
A quantum dual pair（sl２, on) and the associated Capelli Identity, Letters in Mathematical Physics, 34, (1995), 1-8.

[12] T. Hibi and M. Wakayama:
A q-analogue of Capelli's identity for GL(2), Advances in Mathematics, 115, (1995), 49-53.

[11] M. Noumi, T. Umeda and M. Wakayama:
A quantum analogue of the Capelli identity and an elementary differential calculus on GLq(n), Duke Mathematical Journal, 76 (1994), 567-594.

[10] K. Kumahara and M. Wakayama:
On Radon transforms for Minkowski spaces, Journal of the Faculty of General Educations, Tottori Univiversity, 27, (1993), 139-157.

[9] T. Umeda and M. Wakayama:
Powers of 2×2 quantum matrices, Communications in Algebra, 21, (1993), 4461-4465.

[8*] M. Wakayama:
The relation between the η-invariant and the spin representation in terms of the Selberg zeta function, Advanced Studies in Pure Mathematics, 21, (Zeta Functions in Geometry) (1992), 71-86.

[7] M. Wakayama:
A note on the Selberg zeta function for compact quotients of hyperbolic spaces, Hiroshima Mathematical Journal, 21, (1991), 539-555.

[6] T. Oshima, Y. Saburi and M. Wakayama:
Paley-Wiener theorems on a symmetric space and their application, Differential Geometry and Its Applications, 1, (1991), 247-278.

[5] M. Wakayama:
A formula for the logarithmic derivative of Selberg's zeta function, Journal of the Mathematical Society of Japan, 41, (1989), 463-471.

[4] T. Oshima, Y. Saburi and M. Wakayama:
A note on Ehrenpreis' fundamental principle on a symmetric space, Algebraic Analysis, Volume II, (Academic Press) (1988), 681-697.

[3] M. Eguchi and M. Wakayama:
An elementary proof of the Trombi theorem for the Fourier transform of Cp(G:F), Hiroshima Mathematical Journal, 17, (1987), 471-487.

[2] M. Wakayama:
Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Mathematical Journal, 15, (1985), 235-295. (D.‾Sci. Thesis, Hiroshima University).

[1] M. Wakayama:
Zeta functions of Selberg's type for compact quotient of SU(n,1) (n≧2), Hiroshima Mathematical Journal, 14, (1984), 597-618.