Masatoshi Suzuki

Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama, Meguro-ku,
Tokyo 152-8551, Japan


Research Interests

Number theory, analytic properties of zeta functions: classical zeta functions, higher zeta integrals, zeta functions of arithmetic schemes, zeta functions of algebraic groups. Interaction of zeta functions with number theory, algebraic/arithmetic geometry, representation theory, two dimensional canonical systems, functional analysis, harmonic analysis, partial differential equations, integral equations, screw functions, infinitely divisible distributions, value distributions, M-functions.

  ♦ I am here in mathematics genealogy.

Publications

  1. Interpretation of the Schur-Cohn test in terms of canonical systems,
    To appear in Michigan Mathematical Journal.
    A draft is available at arxiv:2106.04061.

  2. Aspects of the screw function corresponding to the Riemann zeta function,
    J. Lond. Math. Soc., early view, (OA).

  3. Li coefficients as norms of functions in a model space,
    J. Number Theory 252 (2023), 177-194.
    A draft is available at arxiv:2301.05779.

  4. (with T. Nakamura) On infinitely divisible distributions related to the Riemann hypothesis,
    Statist. Probab. Lett. 201 (2023), 109889.
    A draft is available at arXiv:2306.08317

  5. An inverse problem for a class of lacunary canonical systems with diagonal Hamiltonian,
    Tohoku Math. J. (2) 74 (2022), no. 4, 549-568.
    A draft is available at arXiv:1907.07838.

  6. Hamiltonian systems arising from L-functions in the Selberg class,
    J. Funct. Anal. 281 (2021), no. 8, 109116 (OA).

  7. An inverse problem for a class of canonical systems having Hamiltonians of determinant one,
    J. Funct. Anal. 279 (2020), no. 12, 108699.
    (This is a revision of arXiv:1606.05726 made by reconstructing
    several parts of the version prior to Oct. 2020.)

  8. Integral operators arising from the Riemann zeta function,
    Various Aspects of Multiple Zeta Functions, 399-411,
    Adv. Stud. Pure Math. 84, Math. Soc. Japan, Tokyo, 2020.
    A draft is available at arXiv:1907.07302

  9. An inverse problem for a class of canonical systems and its applications to self-reciprocal polynomials,
    J. Anal. Math. 136 (2018), no. 1, 273-340.
    A revision after publication is available at arXiv:1308.0228. The corrections for the published version is here.
    (This paper is an upgraded version of the paper "On zeros of self-reciprocal polynomials", which is available in arXiv:1211.2953.)

  10. Nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines,
    Acta Arith. 170 (2015), no. 1, 47-65.
    A draft is available at arXiv:1409.5394

  11. (with H. Ki and Y. Komori) On the zeros of Weng zeta functions for Chevalley groups,
    Manuscripta Math. 148 (2015), no. 1-2, 119-176.
    A draft is available at arXiv:1011.4583

  12. A family of deformations of the Riemann xi-function,
    Acta Arith. 157 (2013), no. 3, 201-230.

  13. (with I. Fesenko and G. Ricotta) Mean-periodicity and zeta functions,
    Annales Inst. Fourier 62 (2012), No. 5, 1819-1887.
    A draft is available at arXiv:0803.2821

  14. Two dimensional adelic analysis and cuspidal automorphic representations of GL(2),
    Multiple Dirichlet Series, L-functions and Automorphic Forms , 339-361,
    Progress in Math., Birkhauser Boston, 2012.
    A draft is available at arXiv:0805.4547

  15. A canonical system of differential equations arising from the Riemann zeta-function,
    Functions in Number Theory and Their Probabilistic Aspects , 397-436,
    RIMS Kokyuroku Bessatsu B34, RIMS, Kyoto, 2012.
    A draft is available at arXiv:1204.1827;
    in the latest version, typos in the published version are corrected.

  16. On monotonicity of certain weighted summatory functions associated with L-functions,
    Comment. Math. Univ. St. Pauli 60 (2011), no. 1-2, 211-225,
    the special volume celebrating Professor Fujii's retirement.
    A draft is available at arXiv:1204.1823

  17. Positivity of certain functions associated with analysis on elliptic surfaces,
    J. Number Theory 131 (2011), no. 10, 1770-1796.
    A draft is available at arXiv:0703052, but its presentation is quite different from the published version.

  18. (with Y. Kamiya) An attempt to interpret the Weil explicit formula from Beurling's spectral theory,
    J. Number Theory 131 (2011), no. 4, 685-704.

  19. (with L. Weng) Zeta functions for G_2 and their zeros,
    Int. Math. Res. Not. IMRN 2009 (2009), no. 2, 241-290.

  20. The Riemann hypothesis for Weng's zeta function of Sp(4) over Q,
    (with an appendix by L. Weng: Zeta functions for Sp(2n)),
    J. Number Theory 129 (2009), no. 3, 551-579.

  21. On the zeros of approximate functions of Rankin-Selberg L-functions,
    Acta Arith. 136 (2009), no. 1, 19-45.

  22. An analogue of the Chowla-Selberg formula for several automorphic L-functions,
    Probability and number theory-Kanazawa 2005, 479-506,
    Adv. Stud. Pure Math. 49, Math. Soc. Japan, Tokyo, 2007.
    A draft is available at arXiv:math/0606096.

  23. A proof of the Riemann hypothesis for the Weng zeta function of rank 3 for the rationals,
    The Conference on L-Functions , 175-199, World Sci. Publ., Hackensack, NJ, 2007.
    A corrected version is available here.

  24. (with J.C. Lagarias) The Riemann hypothesis for certain integrals of Eisenstein series,
    J. Number Theory 118 (2006), no. 1, 98-122.
    An additonal note on functions (24) of this paper is available here.

  25. A relation between the zeros of two different L-functions which have an Euler product and functional equation,
    Int. J. Number Theory 1 (2005), no. 3, 401-429.

  26. (with Y. Kamiya) An asymptotic formula for a sum involving zeros of the Riemann zeta-function,
    Publ. Inst. Math. (Beograd) (N.S.) 76(90) (2004), 81-88.

  27. A relation between the zeros of a L-function belonging to the Selberg class and
    the zeros of an associated L-function twisted by a Dirichlet character,
    Arch. Math. (Basel) 83 (2004), no. 6, 514-527.

 ► Publications in Japanese: here.


Preprints

  1. Analytic theories around the simplest screw,
    arXiv:2308.11860.

  2. (with T. Nakamura) A probabilistic interpretation for central zeros of L-functions in the Selberg class,
    arxiv:2307.02027.

  3. On the Hilbert space derived from the Weil distribution,
    arxiv:2301.00421.

  4. Screw functions of Dirichlet series in the extended Selberg class,
    arxiv:2209.12832.

  5. The screw line of the Riemann zeta-function and its applications,
    arxiv:2209.04658.
    The latest version has been merged into arxiv:2301.00421.

  6. Chains of reproducing kernel Hilbert spaces generated by unimodular functions,
    arXiv:2012.11121.

Conferences

  1. Analytic Number Theory and Related Topics, RIMS, October 15 - 18, 2019.

  2. Analytic Number Theory and Related Topics, RIMS, October 29 - 31, 2018.

  3. Various Aspects of Multiple Zeta Functions, Nagoya University, August 21 - 25, 2017.

  4. French-Japanese Projects "Zeta Functions of Several Variables and Applications",
    Japan-France Research Cooperative Program, 2015-2016.

  5. The 6th Young Mathematicians Conference on Zeta Functions, Nagasaki University, February 15 - 18, 2013.

  6. Zeta Function 2012, Tokyo Institute of Technology, September 24 - 28, 2012.

  7. L-functions of automorphic forms and related problems, The University of Tokyo, March 10 - 13, 2012.

  8. Workshop on various zeta functions and related topics, The University of Tokyo, December 21 - 22, 2010.

 ► Education and Students: here.

Last update: August 24, 2023