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Researcher Information

last modified:2021/10/21

Professor TOHGE Kazuya

Mail

Faculty, Affiliation

Faculty of Electrical, Information and Communication Engineering,Institute of Science and Engineering Basic Mathematical Science
Professor

College and School Educational Field

Division of Electrical Engineering and Computer Science, Graduate School of Natural Science and Technology
Division of Electrical Engineering and Computer Science, Graduate School of Natural Science and Technology
Course in Electrical and Electronic Engineering, School of Electrical, Information and Communication Engineering, College of Science and Engineering

Laboratory

Basic Mathematical Science

Academic Background

Career

Year & Month of Birth

Academic Society

Mathematical Society of Japan
Mathematical Society of Japan

Award

Specialities

Mathematics

Speciality Keywords

Tropical Nevanlinna theory,Theory of Functions

Research Themes

An attempt to apply the value distribution theory to number theory by means of difference.

Trying to develop a 'difference' method to evaluate an equidistribution in view of R. Nevanlinna's value distribution theory but independent of those of meromorphic functions, we hope to understand a variety know such results in number theory in this context and to extend some of them by taking account of the difference of elements in the distribution.

Difference can catch up with differential?

For the purpose to reduce a certain computational complexity, we observe a possibility to replace a role of differential operator by that of difference operator without any approximation and examine to what degree it can be made initially for analytic functions. Then we are going to apply those results in fields of computer technology after rehashing them for piecewise-linear and continuous functions that permit max-plus series expansions.

Tropical value distribution theory and applications

We have extended the Nevanlinna theory on meromorphic functions on the complex plane to the theory on piecewize linear and continuous functions on the real line for the purpose to apply it to the study on ultra-discrete equations.

Study on Value Distribution of Meromorphic or algebroid Functions and holomorphic curves

The research to refine those estimates in the Nevanlinna-Cartan theory on meromorphic or algebroid Functions and holomorphic curves in a complex projective space and to apply them to the related subjects.

Application of the value distribution theory to the study on complex differential and functional eguations

Application of the value distribution theory to the study on complex differential and functional eguations

Study on differential or difference equations appearing in many areas and value distribution of meromorphic functions or holomorphic curves

We apply the value distribution theory of meromorphic functions or holomorphic curves for the study of possible transcendental meromorphic solutions and their systems to differential, (q-)difference or ultradiscrete equations appearing in many areas. Our main subject is to transplant the theory into the corresponding field as in its most suitable formulations.

Books

  •  Risto Korhonen, Ilpo Laine, Kazuya Tohge Tropical value distribution theory and ultra-discrete equations World Scientific Publishing Co. Pte. Ltd. 2015/05
  •  I. Laine and K. Tohge The Bank-Laine conjecture ― a survey Some topics on value distribution and differentiability in complex and p-adic analysis, edited by A. Escassut, W. Tutschke and C.C. Yang, World Scientific Pub. 2009/09

Papers

  •  Dual exponential polynomials and a problem of Ozawa Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge and Zhi-Tao Wen Proceedings of the Royal Society of Edinburgh Section A: Mathematics First View First View 1-19 2021/06/16
  •  A Stothers-Mason theorem with a difference radical Katsuya Ishizaki, Risto Korhonen, Nan Li and Kazuya Tohge Mathematische Zeitschrift 298 1 671-696 2021/05 
  •  Exponential polynomials in the oscillation theory Janne M Heittokangas; Katsuya Ishizaki; Ilpo Laine; Kazuya Tohge Journal of Differential Equations 272 25 911-937 2021/01
  •  Periodicity of meromorphic functions and partial sharing values Weichuan Lin, Kazuya Tohge The Houston Journal of Mathematics  46 3 583-610 2020/12 
  •  A lemma on the difference quotients Risto Korhonen, Kazuya Tohge, Yueyang Zhang, Jinhua Zheng Annales Academiae Scientiarum Fennicae Mathematica 45 1 479-491 2020/01

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  •  Complex oscillation and non-oscillation results Janne Mikael Heittokangas, Katsuya Ishizaki, Ilpo Laine and Kazuya Tohge the Transactions of the American Mathematical Society 372 9 6161-6182 2019/08/05
  •  Tropical Meromorphic Functions in a Finite Interval Ilpo Laine, Kazuya Tohge Annales Academiae Scientiarum Fennicae Mathematica 44 1 341-361 2019/01
  •  Zero distribution and division results for exponential polynomials  Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge, Zhi-Tao Wen The Israel Journal of Mathematics 227 1 397-421 2018/07/21
  •  Meromorphic Functions that Share Four or Five Pairs of Values  Gary G. Gundersen, Norbert Steinmetz, Kazuya Tohge Computational Methods and Function Theory 18 2 239-258 2017/11/28
  •  Tropical variants of some complex analysis results Ilpo Laine, Kai Liu, Kazuya Tohge Annales Academiæ Scientiarum Fennicæ Mathematica 41 923-946 2016/09
  •  Second main theorem in the tropical projective space Risto Korhonen, Kazuya Tohge Advances in Mathematics 298 6 693–725 2016/08
  •  Difference analogue of Cartan's second main theorem for slowly moving periodic targets Risto Korhonen, Nan Li, Kazuya Tohge Annales Academiæ Scientiarum Fennicæ Mathematica 41 523-549 2016/05
  •  Completely regular growth solutions of second order complex linear differential equations Janne Heittokangas, Ilpo Laine, Kazuya Tohge, Zhi-Tao Wen Annales Academiæ Scientiarum Fennicæ Mathematica 40 985-1003 2015/12
  •  Holomorphic curves with shift-invariant hyperplane preimages Rodney Halburd, Risto Korhonen, Kazuya Tohge TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 366 4267-4298 2014/09
  •  The order and type formulas for tropical entire functions – Another flexibility of complex analysis. Kazuya Tohge Reports and Studies in Forestry and Natural Sciences 14 1 113—164 2014/09
  •  Tropical Nevanlinna theory and second main theorem Ilpo Laine, Kazuya Tohge Proceedings of London Mathematical Society 102 5 883-922 2011/04
  •  A unit disc analogue of the Bank-Laine conjecture does not hold Heittokangas J. Annales Academiae Scientiarum Fennicae Mathematica 36 341-351 2011/01
  •  On Gundersen's solution of the Fermat-type functional equation of degree $6$ Complex Variables and Elliptic Equations 56 1 233-251 2010/08
  •  Remarks on a special fundamental solution base and its product Complex Analysis and its Applications, Proceedings of the 15th ICFIDCAA, 2, 351-356 2008/03
  •  Riccati differential equations with elliptic coefficients, II Tohoku Math. J. 55 1 99-108 2003/05
  •  Uniqueness theorems in an angular domain Lin, Weichuan; Mori, Seiki; Tohge, Kazuya TOHOKU MATHEMATICAL JOURNAL 58 4 509-527 2006/11
  •  Complex difference equations of Malmquist type Computational Methods and Function Theory 1 1 27-39 2002/01
  •  Riccati differential equations with elliptic coefficients Result. Math. 32 2 58-71 2000/06
  •  On results of H. Ueda and G. Brosch concerning the unicity of meromorphic functions Han, Qi; Mori, Seiki; Tohge, Kazuya JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 335 2 915-934 2007/02
  •  Logarithmic derivatives of meromorphic or algebroid solutions of some homogeneous linear differential equations International mathematical journal of analysis and its applications: Analysis 19 3 273-297 1999/10
  •  On meromorphic solutions of linear differential equations with at least one transcendental coefficient Proceedings of the 2nd congress Isaac 1999 1 1 399-411 2000/02
  •  On Shared-Value Properties of Painlev\'e Transcendents Lin W. Computational Methods for Function Theory 7 2 477-499 2007/07
  •  Unique range sets for polynomials or rational functions Progress in Analysis: Proceedings of the 3rd ISAAC Congress 1 1 235 - 246 2003/01
  •  Entire and meromorphic solutions of $f^5+g^5+h^5=1$ Univ. Joensuu Dep. Math. Report series 6 57 - 67 2004/05
  •  Some examples of holomorphic curves in $\\P^{n}(\\C)$ extremal to Cartan\'s Proc. of 12th Int. Conference on Finite or Infinite Dimensional Complex Analysis 1 0 387-395 2005/06

Conference Presentations

  • Nevanlinna theory and tropical Nevanlinnatheory(conference:Chinese-Finnish Workshop in Complex Analysis 2019)(2019/08/26)
  • Mason's theorem with a difference radical(conference:Mathematics research seminar)(2019/03/25)
  • Mason's theorem with a difference radical(conference:The joint meeting on theory of conformal mappings and value distribution theory, 2019)(2018/12/08)
  • Mason's theorem with a difference radical(conference:The 26th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) )(2018/07/09)
  • Meromorphic functions that share four or five pairs of values(conference:The International Conference on Computational Methods and Function Theory 2017 (CMFT ’2017))(2017/07/13)

show all

  • Meromorphic functions that share four or five pairs of values(conference:Mathematics research seminar)(2017/03/24)
  • Meromorphic functions that share four or five pairs of values (joint work with Gary G. Gundersen and Norbert Steinmetz) (conference:Joint Meeting on Conformal Mappings and Value Distribution Theory)(2017/01/21)
  • Tropical value distribution on a finite interval(conference:The 23rd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications )(2015/08/15)
  • Periodicity of Meromorphic Functions and Partial Sharing Values(conference:Mathematics research seminar)(2018/03/27)
  • General solution to linear difference equations and a simple algorithm to solve them by piecewise linear and continuous functions(conference:The Mathematics Research Seminar)(2016/03/30)
  • The Order and Type Formulas for Tropical Entire Functions(conference:Mathematics research seminar)(2014/11/18)
  • From Nevanlinna theory and function theory to Tropical Nevanlinna theory and max-plus function theory(2015/02/07)
  • From Nevanlinna’s value distribution theory and function theory to Tropical value distribution theory and max-plus function theory(conference:The mathematical research seminar)(2015/03/30)

Others

Arts and Fieldwork

Patent

Theme to the desired joint research

Grant-in-Aid for Scientific Research

○「差分方程式の複素領域における研究とその応用について 分担基盤C(電情/藤解和也・石崎)* 450,000 」(2020-2022) 
○「分布論をモデルとした複素函数論の超離散的関数論への変換と諸分野への応用」(2016-2018) 
○「トロピカルNevanlinna-Cartan理論の完成と複素解析的手法への還元」(2013-2016) 
○「ネバンリンナ理論の他分野への移植」(2010-2012) 
○「諸分野に現れる微分・差分方程式と有理型函数・正則曲線の値分布に関する研究」(2007-2009) 
○「値分布論と複素力学系を応用した函数方程式の研究」(2003-2003) 
○「値分布論と複素力学系を応用した函数方程式の研究」(2002-2002) 
○「有理型函数と正則曲線の値分布の研究と複素力学系、微分・函数方程式への応用」(2001-2001) 
○「有理型函数と正則曲線の値分布の研究と複素力学系,微分・函数方程式への応用」(2000-2000) 
○「値分布論の応用による複素力学系及び複素微分方程式とその関連分野の研究」(1998-1998) 
○「値分布論の応用による複素力学系及び複素微分方程式とその関連分野の研究」(1997-1997) 

Competitive research funding,Contribution

Collaborative research,Consignment study

Classes (Bachelors)

○Theory of Complex Analysis and Exercise(2020)
○Differential and Integral Calculus 1(2020)
○Differential and Integral Calculus 1(2020)
○Differential and Integral Calculus 1B(2020)
○Differential and Integral Calculus 1A(2020)
○Differential and Integral Calculus 1B(2020)
○Differential and Integral Calculus 1A(2020)
○Theory of Complex Analysis and Exercise(2020)
○Theory of Complex Analysis and Exercise(2020)
○Theory of Differential Equations and Exercise(2020)
○Theory of Differential Equations and Exercise(2020)
○Theory of Differential Equations and Exercise(2020)
○Theory of Differential Equations and Exercise(2020)
○Theory of Differential Equations and Exercise(2020)
○Theory of Complex Analysis and Exercise(2020)
○Differential and Integral Calculus 1(2018)
○Differential and Integral Calculus 1(2018)
○Discrete Mathematics(2018)
○Theory of Complex Analysis and Exercise(2018)
○Discrete Mathematics for Computer Science(2018)
○Theory of Complex Analysis and Exercise(2017)
○Discrete Mathematics(2017)
○Differential and Integral Calculus 1(2017)
○Differential and Integral Calculus 1(2017)
○Back-up practice for Mathematics (2017)
○Differential and Integral Calculus 1(2016)
○Differential and Integral Calculus 1(2016)
○Discrete Mathematics(2016)
○Theory of Complex Analysis and Exercise(2016)
○Back-up practice for Mathematics (2016)

Classes (Graduate Schools)

○Mathematics in Cryptography B(2020)
○Mathematics in Cryptography A(2020)
○Invitation to Discrete Mathematics B(2020)
○Invitation to Discrete Mathematics A(2020)
○Mathematics in Cryptography(2018)
○Invitation to Discrete Mathematics(2018)
○Invitation to Discrete Mathematics(2017)
○Mathematics in Cryptography(2017)
○Nevanlinna Theory and its Applications(2016)
○Mathematics in Cryptography(2016)
○Invitation to Discrete Mathematics(2016)

International Project

International Students

Lecture themes

Others (Social Activities)

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