# Publications

**Preprints**

**Papers**

- [104] Spectral degeneracies in the asymmetric quantum Rabi model, Cid Reyes- Bustos and Masato Wakayama, in ``Mathematical Modelling for Next- Generation Cryptography" eds. T.~Takagi et al., Mathematics for Industry, Springer, 2017 (to appear).
- [103] Equivalence between the eigenvalue problem of non-commutative harmonic oscillators and existence of holomorphic solutions of Heun differential equations, eigenstates degeneration and Rabi model , Masato Wakayama,International Mathematics Research Notices, Pages 759-794, DOI:10.1093/imrn/rnv145, 2016
- [102] Hermitian Symmetric Spaces of Tube Type and Multivariate Meixner-Pollaczek Polynomials, Jacques Faraut and Masato Wakayama, Mathematica Scandinavica, Vol 120(2017), Pages 87-114
- [101] Wreath determinants for group-subgroup pairs(Kei HAMAMOTO, Kazufumi KIMOTO, Kazutoshi TACHIBANA and Masato WAKAYAMA), Journal of Combinatorial Theory, Series A (2015)
- [100] The quantum Rabi model and Lie algebra representations of sl_2, Masato Wakayama and Taishi Yamasaki, Journal of Physics A: Mathematical and Theoretical, 47 (2014).
- [99] Remarks on quantum interaction models by Lie theory and modular forms via non-commutative harmonic oscillators(Masato Wakayama), 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.
- [98] A Lie theoretic proposal on algorithms for the spherical harmonic lighting(Masato Wakayama), Mathematical Progress in Expressive Image Synthesis I-Extended and Selected Results from the Symposium MEIS2013, pp43-54, Series: Mathematics for Industry, Vol. 4, Anjyo, Ken (Ed.) 2014.
- [97] 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.
- [96] Invariant differential operators on the Heisenberg group and Meixner-Pollaczek polynomials, Jacques Faraut & Masato Wakayama, 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.
- [95] Milnor-Selberg zeta functions and zeta regularizations (with Nobushige Kurokawa, Yoshinori Yamasaki) Milnor-Selberg zeta functions and zeta regularizations", J. Geometry and Physics, Volume 64, 2013, Pages 120-145.
- [94] M. Wakayama & K.Yamamoto, "Non-linear algebraic differential equations satisfied by Certain family of elliptic functions", The Ramanujan Journal,February 2013, 30 (2), pg. 173-186.
- [93] K. Kimoto, M. Wakayama, "Spectrum of non-commutative harmonics oscillators and residual modular forms", Noncommutative Geometry and Physics 3, World Scientific (2012), 237-267.
- [92] M. Wakayama, Y. Yamasaki, "Higher regularizations for zeros of cuspidal automorphic L-functions of GL(d)", J. Theo. Nombres Bordeaux, 23,（2011), 751-767
- [91] T. Imai, A. Takaesu, M. Wakayama, "Remarks on geodesics for multivariate normal models", J. Math-for-Industry, (2011B-6), 125-130
- [90] Over the zeta regularized numeration, Preprint 2010(to appear RIMS Kokyuroku) .
- [89] Alpha-determinant cyclic modules and Jacobi polynomials, Transactions of the American Mathematical Society, 361 (2009), 6447-6473, (with Kazufumi Kimoto and Sho Matsumoto).
- [88] Ruelle type $L$-functions versus determinants of Laplacians for torsion free abelian groups, International Journal of Mathematics, 19(8), (2008), 957-979, (with Nobushige Kurokawa and Yoshinori Yamasaki).
- [87] Period deformations and Raabe's formulas for generalized gamma and sine functions, Kyushu Journal of Mathematics, 62, (2008) 171-187 (with Nobushige Kurokawa).
- [86] Invariant theory for singular $\alpha$-determinants, Journal of Combinatorial Theory, Series A, 115, (2008) 1-31 (with Kazufumi Kimoto).
- [85] $q$-Analogues of the Riemann zeta, the Dirichlet $L$-functions and a crystal zeta function, Forum Mathematicum, 20, (2008), 1-26 (with Kenichi Kawagoe and Yoshinori Yamasaki).
- [[84] Elliptic curves arising from the spectral zeta functions for non-commutative harmonic oscillators and $\Gamma_0(4)$-modular forms, Proceedings of the conference on $L$-functions, World Scientific (2007), 201-218 (with Kazufumi Kimoto).
- [83] On the spectral zeta function for the non-commutative harmonic oscillator, Reports on Mathematical Physics, 59, (2007), 421-432 (with Takashi Ichinose).
- [82] Quantum α-determinant cyclic modules of ${\cal U}_q(\frak{gl}_n)$, Journal of Algebra, 313, (2007), 922--956 (with Kazufumi Kimoto).
- [81] Jackson-Mellin's transform of modular forms and $q$-zeta functions, Kyushu Journal of Mathematics, 61, (2007), 551-563 (with Shai Haran and Nobushige Kurokawa).
- [80] Jackson's integral of the Hurwitz zeta function, Rendiconti del Circolo mathemateco di Palermo, 56, (2007), 43-56 (with Nobushige Kurokawa and Katsuhisa Mimachi).
- [79] Splitting density for lifting about discrete groups, Tohoku Mathematical Journal, 59, (2007), 527-545 (with Yasufumi Hashimoto).
- [78] Milnor's multiple gamma functions, Journal of the Ramanujan Mathematical Society, 21, (2006) 153--167 (with Nobushige Kurokawa and Hiroyuki Ochiai).
- [77] Alpha-determinant cyclic modules of $\frak{gl}_n(\Bbb C)$, Journal of Lie Theory, 16, (2006), 393-405 (with Sho Matsumoto).
- [76] Ap\'ery-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] Integral representations of $q$-analogues of the Hurwitz zeta function, Monatshefte f\"ur Mathematik, 149, (2006), 141-154 (with Yoshinori Yamasaki).
- [74] Algebraicity and transcendency of basic special values of Shintani's double sine functions, Proceedings of the Edinburgh Mathematical Society, 49, (2006), 361--366 (with Nobushige Kurokawa).
- [73] Applications of minor summation formulas III, Pl\"ucker relations, Lattice paths and pfaffinas, Journal of Combinatorial Theory, Series A, 113, (2006), 113--155 (with Masao Ishikawa).
- [72] A q-logarithmic analogue of Euler's sine integral, Rendiconti del Seminario Matematico della Universita di Padova, 114, (2005), 51-62 (with Nobushige Kurokawa).
- [71] Gamma and sine functions for Lie groups and period integrals, Indagationes Mathematicae N.S., 16, (2005), 585-607 (with Nobushige Kurokawa).
- [70] Hierarchy of the Selberg zeta functions, Letters in Mathematical Physics, 73, (2005), 59--70 (with Yasufumi Hashimoto).
- [69] Differential algebraicity of multiple sine functions, Letters in Mathematical Physics, 71, (2005), 75--82 (with Nobushige Kurokawa).
- [68] Remarks on Shintani's zeta function, Journal of the Mathematical Sciences, University of Tokyo, 12, (2005), 289--317.
- [67] Multiple finite Riemann zeta functions, Acta Arithmetica, 116, (2005), 173--187 (with Kazufumi Kimoto, Nobushige Kurokawa and Sho Matsumoto).
- [66] 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 (with Takashi Ichinose).
- [65] Zeta functions for the spectrum of the non-commutative harmonic oscillators, Communications in Mathematical Physics, 258, (2005), 697--739 (with Takashi Ichinose).
- [64] Extensions of zeta functions -- examples and a study of the double sine functions, Acta Applicandae Mathematicae, 86, (2005), 179--201 (with Nobushige Kurokawa).
- [63] Regularizations and finite ladders in multiple trigonometry, Journal of the Mathematical Society of Japan, 57, (2005), 1197--1216 (with Nobushige Kurokawa).
- [62] Certain families of elliptic functions defined by $q$-series, The Ramanujan Journal, 10, (2005), 23--41 (with Nobushige Kurokawa).
- [61] Generalized zeta regularizations, quantum class number formulas, and Appell's $O$-functions, The Ramanujan Journal, 10, (2005), 291--303 (with Nobushige Kurokawa).
- [60] Zeta functions of $q$-perfect numbers, Rendiconti del Circolo Mathemateco di Palermo, 53, (2004), 381--389 (with Nobushige Kurokawa).
- [59] Zeta regularizations, Acta Applicandae Mathematicae, 81, (2004), 147--166 (with Nobushige Kurokawa).
- [58] Ruelle type zeta functions for tori and arithmetics, International Journal of Mathematics, 15, (2004), 691--715 (with Nobushige Kurokawa).
- [57] Absolute tensor products, International Mathematics Research Notices, 2004:5, (2004), 249-260 (with Nobushige Kurokawa).
- [56] Zeta regularized products for multiple trigonometric functions, Tokyo Journal of Mathematics, 27, (2004), 459-480 (with Nobushige Kurokawa).
- [55] Extremal values of multiple trigonometric functions, Kyushu Journal of Mathematics, 58, (2004), 141--166 (with Nobushige Kurokawa).
- [54] Remarks on zeta regularized products, International Mathematics Research Notices, 2004:17, (2004), 855-875. (with Kazufumi Kimoto).
- [53] Some examples of generalized zeta regularized products, Kodai Mathematical Journal, 27, (2004), 321-335. (with Kazufumi Kimoto, Nobushige Kurokawa and Chie Sonoki).
- [52] A note on spectral zeta functions of quantum groups, International Journal of Mathematics, 15, (2004), 125-133 (with Nobushige Kurokawa).
- [51] On $q$-analogues of the Euler constant and Lerch's limit formula, Proceedings of the American Mathematical Society, 132, (2004), 935--943 (with Nobushige Kurokawa).
- [50] Euler's constants for the Selberg and the Dedekind zeta functions, Bulletin of the Belgian Mathematical Society Simon Stevin, 11, (2004), 493--516 (with Yasufumi Hashimoto, Yasuyuki Iijima and Nobushige Kurokawa).
- [49] Higher Selberg zeta functions, Communications in Mathematical Physics, 247, (2004), 447--466 (with Nobushige Kurokawa).
- [48] A generalization of Lerch's formula, Czechoslovak Mathematical Journal, 54, (2004), 949--954 (with Nobushige Kurokawa).
- [46] On $q$-basic multiple gamma functions, Interenational Journal of Mathematics, 14, (2003), 885--902 (with Nobushige Kurokawa).
- [45] Duplication formulas in triple trigonometory, Proceedings of the Japan Academy, 79, Ser. A (2003), 123-127 (with Nobushige Kurokawa).
- [44] Gamma factors and functional equations of higher Riemann zeta functions, (with Nobushige Kurokawa, Sachiko Matsuda) Kyushu University Preprint Series in Math. 2003-10.
- [43] Half zeta functions, Journal of the Ramanujan Mathematical Society, 18, (2003), 195--209 (with Miki Hirano, Nobushige Kurokawa).
- [42] Cauchy-Schwarz type inequalities for categories, Kyushu Journal of Mathematics, 57, (2003), 325--331 (with Nobushige Kurokawa).
- [41] Zeta regularizations and $q$-analogue of ring sine functions, Kyushu Journal of Mathematics, 57, (2003), 197--215 (with Kazufumi Kimoto, Nobushige Kurokawa and Chie Sonoki).
- [40] Absolute derivations and zeta functions, Documenta Mathematica, (Extra Volume Kato) (2003), 565--584 (with Nobushige Kurokawa and Hiroyuki Ochiai).
- [39] A variation of Euler's approach to values of the Riemann zeta function, Kyushu Journal of Mathematics, 57, (2003), 175--192 (with Masanobu Kaneko and Nobushige Kurokawa).
- [38] 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), (with Nobushige Kurokawa).
- [37] Corrigenda and remarks to "Non-commutative harmonic oscillators I, Forum Mathematicum, 14, (2002), 539--604 " ibid. 15, (2003), 955--963 (with Alberto Parmeggiani).
- [36] Kronecker's Jugendtraum and ring sine functions, Journal of the Ramanujan Mathematical Society, 17, (2002), 211-220 (with Nobushige Kurokawa, Eva-Marie M\"uller-St\"uler and Hiroyuki Ochiai).
- [35] Multiple trigonometry and zeta functions, Journal of the Ramanujan Mathematical Society, 17, (2002), 101--113 (with Nobushige Kurokawa and Hiroyuki Ochiai).
- [34] Zeta extensions, Proceedings of the Japan Academy, 78, Ser. A (2002), 126--130 (with Nobushige Kurokawa).
- [33]A Remark on systems of differential equations associated with representations of $\frak{sl}_2(\Bbb R)$ and their perturbations, Kodai Mathematical Journal, 25 (2002), 254--277 (with Alberto Parmeggiani).
- [32] Casimir effects on Riemann surfaces, Indagationes Mathematicae N.S. (Koninklijke Nederlandse Akademie van Wetenschappen), 13, (2002), 63--75 (with Nobushige Kurokawa).
- [31] Verified numerical computations of eigenvalue problems for non-commutative harmonic oscillators, Numerical Functional Analysis and Optimization, 23, (2002), 633--650 (with Kaori Nagatou, Mitsuhiro T. Nakao).
- [30] Non-commutative harmonic oscillators II, Forum Mathematicum, 14, (2002), 669--690 (with Alberto Parmeggiani).
- [29] Equidstribution of holonomy restricted to a homology class about closed geodesics, Forum Mathematicum, 14, (2002), 383--403 (with Kazufumi Kimoto).
- [28] Explicit Capelli Identities for skew symmetric matrices, Proceedings of the Edinburgh Mathematical Society, 45, (2002), 449--465 (with Kenji Kinoshita).
- [27] Non-commutative harmonic oscillators I, Forum Mathematicum, 14, (2002), 539--604 (with Alberto Parmeggiani).
- [26] On $\zeta(3)$, Journal of the Ramanujan Mathematical Society, 16, (2001), 205--214 (with Nobushige Kurokawa).
- [25] 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 (with Alberto Parmeggiani).
- [24] A formula for the multiplicity of the principal series in $L^2(\Gamma\backslash G)$, Forum Mathematicum, 12, (2000), 757-766 (with Nobushige Kurokawa and Hitodakari Kuroyama).
- [23] Minor summation formulas of Paffians, Survey and a new identity, Advanced Studies in Pure Mathematics, 28, (Combinatorial Methods in Representation Theory) (2000), 133--142 (with Masao Ishikawa).
- [22] Applications of minor summation formulas II, Pfaffians and Schur Polynomials, Journal of Combinatorial Theory, Series A, 88, (1999), 136--157 (with Masao Ishikawa).
- [21] Equidistribution of holonomy about closed geodesics, Duke Mathematical Journal, 100, (1999), 1--57 (with Peter Sarnak).
- [20] 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] New Schur function series, Journal of Algebra, 208, (1998), 480--525 (with Masao Ishikawa).
- [18] Another look at the differential operators on the quantum matrix spaces and its applications, Commentarii Mathematici Universitatis Sancti Pauli, 47 (1998), 53--80 (with Tôru Umeda).
- [17] Applications of minor summation formulas I, Littlewood's formulas, Journal of Algebra, 183, (1996), 193--216 (with Masao Ishikawa and Soichi Okada).
- [16] Dual pairs, spherical harmonics and a Capelli Identity in quantum group theory, Compositio Mathematica, 104, (1996), 227--277 (with Masatoshi Noumi and Tôru Umeda).
- [15] Minor summation formula of Pfaffians and Schur functions' identities, Proceedings of the Japan Academy, 71A, (1995), 54--57 (with Masao Ishikawa).
- [14] Minor summation formula of Pfaffians , Linear and Multilinear Algebra, 39 (1995), 285--305 (with Masao Ishikawa).
- [13] A quantum dual pair $(\frak{sl}_2, \frak{o}_n)$ and the associated Capelli Identity, Letters in Mathematical Physics, 34, (1995), 1--8 (with Masatoshi Noumi and Tôru Umeda).
- [12] A $q$-analogue of Capelli's identity for $GL(2)$, Advances in Mathematics, 115, (1995), 49--53 (with Takayuki Hibi).
- [11] A quantum analogue of the Capelli identity and an elementary differential calculas on $GL_q(n)$, Duke Mathematical Journal, 76 (1994), 567--594 (with Masatoshi Noumi and Tôru Umeda).
- [10] On Radon transforms for Minkowski spaces, Journal of the Faculty of General Educations, Tottori Univiversity, 27, (1993), 139--157 (with Keisaku Kumahara).
- [9] Powers of $2\times 2$ quantum matrices, Communications in Algebra, 21, (1993), 4461--4465 (with Tôru Umeda).
- [8] The relation between the $\eta$-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] A note on the Selberg zeta function for compact quotients of hyperbolic spaces, Hiroshima Mathematical Journal, 21, (1991), 539--555.
- [6] Paley-Wiener theorems on a symmetric space and their application, Differential Geometry and Its Applications, 1, (1991), 247--278 (with Toshio Oshima and Yutaka Saburi).
- [5] A formula for the logarithmic derivative of Selberg's zeta function, Journal of the Mathematical Society of Japan, 41, (1989), 463--471.
- [4] A note on Ehrenpreis' fundamental principle on a symmetric space, Algebraic Analysis, Volume II, (Academic Press) (1988), 681--697 (with Toshio Oshima and Yutaka Saburi).
- [3] An elementary proof of the Trombi theorem for the Fourier transform of $C^p(G:F)$, Hiroshima Mathematical Journal, 17, (1987), 471--487 (with Masaaki Eguchi).
- [2] Zeta functions of Selberg's type associated with homogeneous vector bundles, Hiroshima Mathematical Journal, 15, (1985), 235--295. (D.~Sci. Thesis, Hiroshima University).
- [1] Zeta functions of Selberg's type for compact quotient of $SU(n, 1)\, (n\geq2)$, Hiroshima Mathematical Journal, 14, (1984), 597--618.

**Books**

- [9] "Importance and Unpredictable Effectiveness of Mathematics in the Real World and for Industry", What Mathematics Can Do for You, Giga, Yoshikazu; Kobayashi, Toshiyuki (Eds.), 101-121, Springer, 2013.
- [8] Importance and Unpredictable Effectiveness of Mathematics in the Real-World and for Industry, Masato Wakayama, 数学は役に立っているか？, Springer, 2012.
- [7] Wakayama, Masato: Interfacing Educational & Research with Mathematics-for-Industry: The Endeavour in Japan. In: Damlamian, A., J.-F. Rodrigues, et al. (to appear in 2012). Educational Interfaces between Mathematics and Industry (EIMI). An ICMI-ICIAM Study 20. Berlin - Heidelberg, Springer.
- [6] Casimir Force, Casimir Operators and the Riemann Hypothesis--Mathematics for Innovation in Industry and Science--, Editor, with Gerrit van Dijk , De Gruyter, 2010．
- [5]Visualization and Modern Geometry, Iwanami Publishers, Tokyo, 2010．
- [4] Mathematics for Modern Industrial Technology (6 volumes), Editor, Kodansha, Tokyo, 2008〜．
- [3] Contemporary Mathematics in Technology, Iwanami Publishers, Tokyo, 2008, Editor,（Coauthers: Y. Ninomiya, S. Taniguchi, M. Kaneko, Y. Fukumoto, O. Saeki）.
- [2] Absolute Casimir Elements, Iwanami Publishers, Tokyo, 2002（Coauther: S. Kurokawa）.
- [1] Zeta's World, Nippon Hyoronsha Publishers, Tokyo, 1999（Coauthers: T. Umeda, S. Kurokawa, S. Nakajima).

**Other Articles**

- [1]Wakayama, Masato: Interfacing Educational & Research with Mathematics-for-Industry: The Endeavour in Japan. In: Damlamian, A., J.-F. Rodrigues, et al. (to appear in 2012). Educational Interfaces between Mathematics and Industry (EIMI). An ICMI-ICIAM Study 20. Berlin - Heidelberg, Springer.