Masatoshi Suzuki
Department of Mathematics
Tokyo Institute of Technology
2121 Ookayama, Meguroku,
Tokyo 1528551, 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.
♦ I am
here in
mathematics genealogy.
Publications

Chains of reproducing kernel Hilbert spaces generated by unimodular functions,
To appear in Annales de l'Institut Fourier.
A draft is available at
arXiv:2012.11121.

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

Aspects of the screw function corresponding to
the Riemann zeta function,
J. Lond. Math. Soc. 108 (2023), no.4, 14481487 (OA).

Li coefficients as norms of functions in a model space,
J. Number Theory 252 (2023), 177194.
A draft is available at
arxiv:2301.05779.

(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

An inverse problem for a class of lacunary canonical systems with diagonal Hamiltonian,
Tohoku Math. J. (2) 74 (2022), no. 4, 549568.
A draft is available at
arXiv:1907.07838.

Hamiltonians arising from Lfunctions in the Selberg class,
J. Funct. Anal. 281 (2021), no. 8, 109116 (OA).

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, 399411,
Adv. Stud. Pure Math. 84, Math. Soc. Japan, Tokyo, 2020.
A draft is available at
arXiv:1907.07302

An inverse problem for a class of canonical systems and its applications to selfreciprocal polynomials,
J. Anal. Math. 136 (2018), no. 1, 273340.
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 selfreciprocal polynomials",
which is available in
arXiv:1211.2953.)

Nearest neighbor spacing distributions for the zeros of the real
or imaginary part of the Riemann xifunction on vertical lines,
Acta Arith. 170 (2015), no. 1, 4765.
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. 12, 119176.
A draft is available at
arXiv:1011.4583

A family of deformations of the Riemann xifunction,
Acta Arith. 157 (2013), no. 3, 201230.

(with I. Fesenko and G. Ricotta)
Meanperiodicity and zeta functions,
Annales Inst. Fourier 62 (2012), No. 5, 18191887.
A draft is available at
arXiv:0803.2821

Two dimensional adelic analysis and cuspidal automorphic representations of GL(2),
Multiple Dirichlet Series, Lfunctions and Automorphic Forms , 339361,
Progress in Math., Birkhauser Boston, 2012.
A draft is available at
arXiv:0805.4547

A canonical system of differential equations arising from the Riemann zetafunction,
Functions in Number Theory and Their Probabilistic Aspects , 397436,
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 Lfunctions,
Comment. Math. Univ. St. Pauli 60 (2011), no. 12, 211225,
the special volume celebrating Professor Fujii's retirement.
A draft is available at
arXiv:1204.1823

Positivity of certain functions associated with analysis on elliptic surfaces,
J. Number Theory 131 (2011), no. 10, 17701796.
A draft is available at
arXiv:0703052, but its presentation is quite different from the published version.

(with Y. Kamiya)
An attempt to interpret the Weil explicit formula from Beurling's spectral theory,
J. Number Theory 131 (2011), no. 4, 685704.

(with L. Weng)
Zeta functions for G_2 and their zeros,
Int. Math. Res. Not. IMRN 2009 (2009), no. 2, 241290.

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, 551579.

On the zeros of approximate functions of RankinSelberg Lfunctions,
Acta Arith. 136 (2009), no. 1, 1945.

An analogue of the ChowlaSelberg formula for several automorphic Lfunctions,
Probability and number theoryKanazawa 2005, 479506,
Adv. Stud. Pure Math. 49, Math. Soc. Japan, Tokyo, 2007.
A draft is available at
arXiv:math/0606096.

A proof of the Riemann hypothesis for the Weng zeta function of rank 3 for the rationals,
The Conference on LFunctions , 175199, World Sci. Publ., Hackensack, NJ, 2007.
A corrected version is available here.

(with J.C. Lagarias)
The Riemann hypothesis for certain integrals of Eisenstein series,
J. Number Theory 118 (2006), no. 1, 98122.
An additonal note on functions (24) of this paper is available here.

A relation between the zeros of two different Lfunctions which have an Euler product and functional equation,
Int. J. Number Theory 1 (2005), no. 3, 401429.

(with Y. Kamiya)
An asymptotic formula for a sum involving zeros of the Riemann zetafunction,
Publ. Inst. Math. (Beograd) (N.S.) 76(90) (2004), 8188.

A relation between the zeros of a Lfunction belonging to the Selberg class and
the zeros of an associated Lfunction twisted by a Dirichlet character,
Arch. Math. (Basel) 83 (2004), no. 6, 514527.
► Publications in Japanese:
here.
Preprints

Analytic theories around the simplest screw,
arXiv:2308.11860.

(with T. Nakamura)
A probabilistic interpretation for central zeros of Lfunctions 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.

The screw line of the Riemann zetafunction and its applications,
arxiv:2209.04658.
The latest version has been merged into
arxiv:2301.00421.
Conferences

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

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

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

FrenchJapanese Projects "Zeta Functions of Several Variables and Applications",
JapanFrance Research Cooperative Program, 20152016.

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.

Lfunctions of automorphic forms and related problems,
The University of Tokyo, March 10  13, 2012.

Workshop on various zeta functions and related topics,
The University of Tokyo, December 21  22, 2010.
► Education and Students:
here.
Last update: October 6, 2023