Singular Stochastic Dispersive Dynamics

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Publications

Sharp quasi-invariance threshold for the cubic Szegő equation

Author(s): James Coe, Leonardo Tolomeo
Published in: 2024
Publisher: arXiv

On the inviscid limit of the singular stochastic complex Ginzburg-Landau equation at statistical equilibrium

Author(s): Younes Zine
Published in: 2022
Publisher: arXiv

Norm inflation with infinite loss of regularity for the generalized improved Boussinesq equation

Author(s): Pierre de Roubin
Published in: 2023
Publisher: arXiv

Global well-posedness of one-dimensional cubic fractional nonlinear Schrödinger equations in negative Sobolev spaces

Author(s): Enguerrand Brun, Guopeng Li, Ruoyuan Liu, Younes Zine
Published in: 2023
Publisher: arXiv

Revisiting Bourgain's probabilistic construction of solutions to the 2-d cubic NLS

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: 2025
Publisher: arXiv

Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation

Author(s): Guopeng Li, Jiawei Li, Tadahiro Oh, Nikolay Tzvetkov
Published in: 2025
Publisher: arXiv

Sharp unconditional well-posedness of the 2-d periodic cubic hyperbolic nonlinear Schrödinger equation

Author(s): Engin Başakoğlu, Tadahiro Oh, Yuzhao Wang
Published in: 2025
Publisher: arXiv

Refined global well-posedness for the periodic modulated Korteweg-de Vries equation

Author(s): Damiano Greco, Massimilano Gubinelli, Shao Liu, Tadahiro Oh
Published in: 2026
Publisher: The University of Edinburgh

Hyperbolic sine-Gordon model beyond the first threshold

Author(s): Younes Zine
Published in: 2025
Publisher: arXiv

Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation

Author(s): Justin Forlano
Published in: 2025
Publisher: arXiv

Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc

Author(s): Justin Forlano, Yuzhao Wang
Published in: 2025
Publisher: arXiv

Fourier restriction norm method adapted to controlled paths: stochastic wave equations

Author(s): Andreia Chapouto, Jiawei Li, Tadahiro Oh
Published in: 2026
Publisher: The University of Edinburgh

Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation

Author(s): Andreia Chapouto, Guopeng Li, Tadahiro Oh
Published in: 2024
Publisher: arXiv

Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic Φ^4_3-model

Author(s): Ruoyuan Liu, Nikolay Tzvetkov, Yuzhao Wang
Published in: 2023
Publisher: arXiv

Stochastic complex Ginzburg-Landau equation on compact surfaces

Author(s): Tristan Robert, Younes Zine
Published in: 2025
Publisher: arXiv

Hyperbolic O(N) linear sigma model and its mean-field limit

Author(s): Ruoyuan Liu, Shao Liu, Tadahiro Oh
Published in: 2025
Publisher: arXiv

Stochastic quantization of Liouville conformal field theory

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov, Yuzhao Wang
Published in: 2020
Publisher: arXiv

Invariant measures for mKdV and KdV in infinite volume

Author(s): Justin Forlano, Rowan Killip, Monica Visan
Published in: 2024
Publisher: arXiv

Shallow-water convergence of the intermediate long wave equation in L^2

Author(s): Andreia Chapouto, Guopeng Li, Tadahiro Oh, Tengfei Zhao
Published in: 2025
Publisher: arXiv

Optimal divergence rate of the focusing Gibbs measure

Author(s): Guopeng Li, Rui Liang, Yuzhao Wang
Published in: 2023
Publisher: arXiv

Nonlinear PDEs with modulated dispersion II: Korteweg--de Vries equation

Author(s): Khalil Chouk, Massimiliano Gubinelli, Guopeng Li, Jiawei Li, Tadahiro Oh
Published in: 2024
Publisher: arXiv

On the singular nature of shallow-water convergence of the intermediate long wave equation on the real line

Author(s): Andreia Chapouto, Benjamin Harrop-Griffiths, Guopeng Li, Tadahiro Oh
Published in: 2026
Publisher: arXiv

Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus

Author(s): Guopeng Li, Mamoru Okamoto, Liying Tao
Published in: 2024
Publisher: arXiv

Nonlinear PDEs with modulated dispersion IV: normal form approach and unconditional uniquenes

Author(s): Massimilano Gubinelli, Guopeng Li, Jiawei Li, Tadahiro Oh
Published in: 2025
Publisher: arXiv

Nonlinear PDEs with modulated dispersion III: multiplicative noises

Author(s): Andreia Chapouto, Massimilano Gubinelli, Guopeng Li, Jiawei Li, Tadahiro Oh
Published in: 2026
Publisher: The University of Edinburgh

A remark on randomization of a general function of negative regularity

Author(s): Tadahiro Oh, Mamoru Okamoto, Oana Pocovnicu, Nikolay Tzvetkov
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 538-554, ISSN 2330-1511
Publisher: American Mathematical Society
DOI: 10.1090/bproc/241

Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

Author(s): Ruoyuan Liu
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 12, 2024, Page(s) 898-931, ISSN 2194-0401
Publisher: Springer
DOI: 10.1007/s40072-023-00297-7

A simple construction of the sine‐Gordon model via stochastic quantization

Author(s): Massimiliano Gubinelli, Martin Hairer, Tadahiro Oh, Younes Zine
Published in: Journal of the London Mathematical Society, Issue 112, 2025, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.70214

Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity $$\overline{u}^2$$ in Negative Sobolev Spaces

Author(s): Ruoyuan Liu
Published in: Journal of Dynamics and Differential Equations, 2023, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-023-10295-x

Global Dynamics for the Two-dimensional Stochastic Nonlinear Wave Equations

Author(s): Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh, Leonardo Tolomeo
Published in: International Mathematics Research Notices, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab084

On global well-posedness of the modified KdV equation in modulation spaces

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: Discrete & Continuous Dynamical Systems, Issue 41/6, 2021, Page(s) 2971, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2020393

Norm Inflation for the Cubic Nonlinear Heat Equation above the Scaling Critical Regularity

Author(s): Ilya Chevyrev, Tadahiro Oh, Yuzhao Wang
Published in: Funkcialaj Ekvacioj, Issue 68, 2025, Page(s) 145-164, ISSN 0532-8721
Publisher: Mathematical Society of Japan
DOI: 10.1619/fesi.68.145

Discrete bilinear operators and commutators

Author(s): Árpád Bényi, Tadahiro Oh
Published in: The Journal of Geometric Analysis, Issue 33, 2023, ISSN 1559-002X
Publisher: Springer
DOI: 10.1007/s12220-022-01136-2

Norm inflation for the derivative nonlinear Schrödinger equation

Author(s): Yuzhao Wang, Younes Zine
Published in: Comptes Rendus. Mathématique, Issue 362, 2025, Page(s) 1857-1871, ISSN 1778-3569
Publisher: Mersenne Center for open scientific publishing
DOI: 10.5802/crmath.566

Almost conservation laws for stochastic nonlinear Schrödinger equations

Author(s): Kelvin Cheung, Guopeng Li, Tadahiro Oh
Published in: Journal of Evolution Equations, Issue 21/2, 2021, Page(s) 1865-1894, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-020-00659-x

On the two-dimensional hyperbolic stochastic sine-Gordon equation

Author(s): Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 9/1, 2021, Page(s) 1-32, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-020-00165-8

A Remark on the Log-Sobolev Inequality for the Gibbs Measure of the Focusing Schrödinger Equation

Author(s): Guopeng Li, Jiawei Li, Leonardo Tolomeo
Published in: Journal of Dynamics and Differential Equations, 2026, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-026-10509-y

Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

Author(s): Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia
Published in: Probability Theory and Related Fields, Issue 189, 2024, Page(s) 1161-1218, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-024-01288-y

Fractional Leibniz rule on the torus

Author(s): Árpád Bényi, Tadahiro Oh, Tengfei Zhao
Published in: Proceedings of the American Mathematical Society, Issue 153, 2024, Page(s) 207-221, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/17007

Intermediate long wave equation in negative Sobolev spaces

Author(s): Andreia Chapouto, Justin Forlano, Guopeng Li, Tadahiro Oh, Didier Pilod
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 452-468, ISSN 2330-1511
Publisher: American Mathematica Society
DOI: 10.1090/bproc/206

Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus

Author(s): Andreia Chapouto, Guopeng Li, Ruoyuan Liu
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2024, Page(s) 1-39, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2024.87

Global well-posedness of the energy-critical stochastic nonlinear wave equations

Author(s): Enguerrand Brun, Guopeng Li, Ruoyuan Liu
Published in: Journal of Differential Equations, Issue 397, 2024, Page(s) 316-348, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2024.03.032

Global dynamics for the stochastic KdV equation with white noise as initial data

Author(s): Tadahiro Oh, Jeremy Quastel, Philippe Sosoe
Published in: Transactions of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 420-460, ISSN 2330-0000
Publisher: American Mathematical Society
DOI: 10.1090/btran/178

Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise

Author(s): Tadahiro Oh, Yuzhao Wang, Younes Zine
Published in: Stochastics and Partial Differential Equations: Analysis and Computations volume, Issue 21940401, 2022, ISSN 2194-0401
Publisher: Springer
DOI: 10.1007/s40072-022-00237-x

Compact bilinear operators and paraproducts revisited

Author(s): Árpád Bényi, Guopeng Li, Tadahiro Oh, Rodolfo H. Torres
Published in: Canadian Mathematical Bulletin, Issue 68, 2025, Page(s) 44-59, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s000843952400047x

Invariant Gibbs dynamics for the dynamical sine-Gordon model

Author(s): Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Issue 151/5, 2021, Page(s) 1450-1466, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2020.68

Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction

Author(s): Jeffrey Kuan, Tadahiro Oh, Sunčica Čanić
Published in: Applicable Analysis, Issue 101, 2022, Page(s) 4349-4373, ISSN 0003-6811
Publisher: Taylor & Francis
DOI: 10.1080/00036811.2022.2103682

On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity |u|^2

Author(s): Ruoyuan Liu
Published in: Journal de Mathématiques Pures et Appliquées, Issue 171, 2023, Page(s) 75-101, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2022.12.010

Comparing the stochastic nonlinear wave and heat equations: a case study

Author(s): Tadahiro Oh, Mamoru Okamoto
Published in: Electronic Journal of Probability, Issue 26/none, 2021, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-ejp575

Solving the 4NLS with white noise initial data

Author(s): Tadahiro Oh, Nikolay Tzvetkov, Yuzhao Wang
Published in: Forum of Mathematics, Sigma, Issue 8, 2020, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2020.51

On the Parabolic and Hyperbolic Liouville Equations

Author(s): Tadahiro Oh, Tristan Robert, Yuzhao Wang
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04125-8

A continuum of invariant measures for the periodic KdV and mKdV equations

Author(s): Andreia Chapouto, Justin Forlano
Published in: Transactions of the American Mathematical Society, Issue 378, 2026, Page(s) 7247-7286, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9489

Hyperbolic $$P(\Phi )_2$$-model on the Plane

Author(s): Tadahiro Oh, Leonardo Tolomeo, Yuzhao Wang, Guangqu Zheng
Published in: Communications in Mathematical Physics, Issue 407, 2026, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-025-05486-0

Critical threshold for weakly interacting log-correlated focusing Gibbs measures

Author(s): Damiano Greco, Tadahiro Oh, Liying Tao, Leonardo Tolomeo
Published in: Proceedings of the American Mathematical Society, Series B, Issue 12, 2026, Page(s) 150-165, ISSN 2330-1511
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/bproc/268

Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

Author(s): Tadahiro Oh, Philippe Sosoe, Leonardo Tolomeo
Published in: Inventiones mathematicae, Issue 00209910, 2022, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01080-y

A note on products of stochastic objects

Author(s): Tadahiro Oh, Younes Zine
Published in: Kyoto Journal of Mathematics, Issue 65, 2025, ISSN 2156-2261
Publisher: Duke University Press
DOI: 10.1215/21562261-2024-0023

Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity

Author(s): Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh
Published in: Journal of the European Mathematical Society, 2023, ISSN 1435-9863
Publisher: EMS Press
DOI: 10.4171/jems/1294

Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations

Author(s): Justin Forlano, Leonardo Tolomeo
Published in: Journal of the European Mathematical Society, 2025, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1643

Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions

Author(s): Trishen S. Gunaratnam, Tadahiro Oh, Nikolay Tzvetkov, Hendrik Weber
Published in: Probability and Mathematical Physics, Issue 26900998, 2022, ISSN 2690-0998
Publisher: Mathematical Science Publishers
DOI: 10.2140/pmp.2022.3.343

A remark on triviality for the two-dimensional stochastic nonlinear wave equation

Author(s): Tadahiro Oh, Mamoru Okamoto, Tristan Robert
Published in: Stochastic Processes and their Applications, Issue 130/9, 2020, Page(s) 5838-5864, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2020.05.010

Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation

Author(s): Guopeng Li, Liying Tao, Tengfei Zhao
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, 2025, ISSN 2194-0401
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40072-025-00389-6

Stochastic nonlinear wave dynamics on compact surfaces

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov
Published in: Annales Henri Lebesgue, Issue 6, 2023, Page(s) 161-223, ISSN 2644-9463
Publisher: École Normale Supérieure de Rennes
DOI: 10.5802/ahl.163

On the two-dimensional singular stochastic viscous nonlinear wave equations

Author(s): Ruoyuan Liu, Tadahiro Oh
Published in: Comptes Rendus Mathématique, Issue 360, 2022, Page(s) 1227-1248, ISSN 1778-3569
Publisher: Académie des sciences, Institut de France
DOI: 10.5802/crmath.377

Smoluchowski-Kramers approximation for singular stochastic wave equations in two dimensions

Author(s): Younes Zine
Published in: Electronic Journal of Probability, Issue 30, 2025, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/25-ejp1337

Deep-water and shallow-water limits of the intermediate long wave equation

Author(s): Guopeng Li
Published in: Nonlinearity, Issue 37, 2024, Page(s) 075001, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad4843

On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing

Author(s): Jingyu Huang, Tadahiro Oh, Mamoru Okamoto
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 378-389, ISSN 2330-1511
Publisher: American Mathematical Society
DOI: 10.1090/bproc/226

Symbolic Calculus for a Class of Pseudodifferential Operators with Applications to Compactness

Author(s): Árpád Bényi, Tadahiro Oh, Rodolfo H. Torres
Published in: The Journal of Geometric Analysis, Issue 35, 2025, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-025-02128-8

Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces

Author(s): Tadahiro Oh, Oana Pocovnicu, Nikolay Tzvetkov
Published in: Annales de l'Institut Fourier, Issue 03730956, 2022, ISSN 0373-0956
Publisher: Association des Annales de I'Institut Fourier
DOI: 10.5802/aif.3454

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces

Author(s): Tadahiro Oh, Kihoon Seong
Published in: Journal of Functional Analysis, Issue 281/9, 2021, Page(s) 109150, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109150

Sharp local well-posedness of the two-dimensional periodic nonlinear Schr&ouml;dinger equation with a quadratic nonlinearity $|u|^2$

Author(s): Ruoyuan Liu, Tadahiro Oh
Published in: Mathematical Research Letters, Issue 31, 2024, Page(s) 255-277, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.240904213416

Deep-water limit of the intermediate long wave equation in $L^2$

Author(s): Andreia Chapouto, Guopeng Li, Tadahiro Oh, Didier Pilod
Published in: Mathematical Research Letters, Issue 31, 2025, Page(s) 1655-1692, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.250210231602

Compact T(1) theorem à la Stein

Author(s): Árpád Bényi, Guopeng Li, Tadahiro Oh, Rodolfo H. Torres
Published in: Journal of Functional Analysis, Issue 289, 2025, Page(s) 111052, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2025.111052

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Author(s): Guopeng Li, Tadahiro Oh, Guangqu Zheng
Published in: Transactions of the London Mathematical Society, Issue 12, 2026, ISSN 2052-4986
Publisher: Wiley
DOI: 10.1112/tlm3.70005

Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation

Author(s): Tadahiro Oh, Mamoru Okamoto, Nikolay Tzvetkov
Published in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Issue 60, 2024, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/23-aihp1380

A remark on Gibbs measures with log-correlated Gaussian fields

Author(s): Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo
Published in: Forum of Mathematics, Sigma, Issue 12, 2024, Page(s) 1-40, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2024.28

Norm inflation for the viscous nonlinear wave equation

Author(s): Pierre de Roubin, Mamoru Okamoto
Published in: Nonlinear Differential Equations and Applications NoDEA, Issue 31, 2024, ISSN 1021-9722
Publisher: Birkhauser Verlag
DOI: 10.1007/s00030-024-00944-5

Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations

Author(s): Andreia Chapouto, Nobu Kishimoto
Published in: Transactions of the American Mathematical Society`, Issue 375, 2022, Page(s) 8483-8528, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8699

Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation

Author(s): Justin Forlano, Leonardo Tolomeo
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, 2025, ISSN 2194-0401
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40072-025-00407-7

Unconditional deep-water limit of the intermediate long wave equation in low-regularity

Author(s): Justin Forlano, Guopeng Li, Tengfei Zhao
Published in: Nonlinear Differential Equations and Applications NoDEA, Issue 32, 2025, ISSN 1021-9722
Publisher: Birkhauser Verlag
DOI: 10.1007/s00030-025-01037-7

Stochastic Quantization of the ³₃-Model

Author(s): Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
Published in: Memoirs of the European Mathematical Society, Issue 16, 2025, ISSN 2747-9099
Publisher: EMS Press
DOI: 10.4171/mems/16

Focusing Φ⁴₃-model with a Hartree-type Nonlinearity

Author(s): Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
Published in: Memoirs of the American Mathematical Society, Issue 304, 2025, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.1090/memo/1529

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