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
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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.
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Aspects of the screw function corresponding to
the Riemann zeta function,
J. Lond. Math. Soc., early view, (OA).
-
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.
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(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
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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.
-
Hamiltonian systems arising from L-functions in the Selberg class,
J. Funct. Anal. 281 (2021), no. 8, 109116 (OA).
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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.)
-
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
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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.)
-
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
-
(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
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A family of deformations of the Riemann xi-function,
Acta Arith. 157 (2013), no. 3, 201-230.
-
(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
-
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
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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.
-
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
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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.
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(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.
-
(with L. Weng)
Zeta functions for G_2 and their zeros,
Int. Math. Res. Not. IMRN 2009 (2009), no. 2, 241-290.
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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.
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On the zeros of approximate functions of Rankin-Selberg L-functions,
Acta Arith. 136 (2009), no. 1, 19-45.
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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.
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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.
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(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.
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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.
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(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.
-
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
-
Analytic theories around the simplest screw,
arXiv:2308.11860.
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(with T. Nakamura)
A probabilistic interpretation for central zeros of L-functions in the Selberg class,
arxiv:2307.02027.
-
On the Hilbert space derived from the Weil distribution,
arxiv:2301.00421.
-
Screw functions of Dirichlet series in the extended Selberg class,
arxiv:2209.12832.
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The screw line of the Riemann zeta-function and its applications,
arxiv:2209.04658.
The latest version has been merged into
arxiv:2301.00421.
-
Chains of reproducing kernel Hilbert spaces generated by unimodular functions,
arXiv:2012.11121.
Conferences
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Analytic Number Theory and Related Topics,
RIMS, October 15 - 18, 2019.
-
Analytic Number Theory and Related Topics,
RIMS, October 29 - 31, 2018.
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Various Aspects of Multiple Zeta Functions,
Nagoya University, August 21 - 25, 2017.
-
French-Japanese Projects "Zeta Functions of Several Variables and Applications",
Japan-France Research Cooperative Program, 2015-2016.
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The 6th Young Mathematicians Conference on Zeta Functions,
Nagasaki University, February 15 - 18, 2013.
-
Zeta Function 2012,
Tokyo Institute of Technology, September 24 - 28, 2012.
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L-functions of automorphic forms and related problems,
The University of Tokyo, March 10 - 13, 2012.
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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