Miyazaki Takafumi 宮崎隆史

Researcher Number	20706725
Other IDs
Affiliation (Current)	2025: 群馬大学, 大学院理工学府, 准教授
Affiliation (based on the past Project Information) *help	2018 – 2024: 群馬大学, 大学院理工学府, 准教授 2016 – 2017: 群馬大学, 大学院理工学府, 助教
Review Section/Research Field	Principal Investigator Basic Section 11010:Algebra-related / Algebra
Keywords	Principal Investigator 単数方程式 / 指数型不定方程式 / 代数的無理数の有理近似 / 対数一次形式の理論 / ベキ剰余理論 / Bakerの手法 / ラマヌジャン・ナゲール型方程式 / 一般化されたフェルマー方程式 / 部分空間定理 / ピライ型方程式 … More / 連立ぺル方程式 / Ramanujan-Nagell 方程式 / 線形回帰数列 / 寺井予想 / 連立ペル方程式 / ディオファントスの組 / Jesmanowicz予想 Less

Research Projects
(3 results)
Research Products
(25 results)

Effective rational approximation to algebraic irrationals and exponential Diophantine equationsPrincipal Investigator
- Principal Investigator
  
  宮崎隆史
- Project Period (FY)
  2024 – 2028
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Gunma University
Algebraic and analytic study on exponential equations related to Fermat's equationPrincipal Investigator
- Principal Investigator
  
  Miyazaki Takafumi
- Project Period (FY)
  2020 – 2023
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Gunma University
Diophantine problems related to polynomial-exponential equationsPrincipal Investigator
- Principal Investigator
  
  Miyazaki Takafumi
- Project Period (FY)
  2016 – 2019
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Gunma University

All 2024 2023 2022 2021 2020 2019 2018 2017 2016

All Journal Article Presentation

[Journal Article] Number of solutions to a special type of unit equations in two unknowns2024
- Author(s)
  Takafumi Miyazaki, Istvan Pink
- Journal Title
  
  American Journal of Mathematics
  
  Volume: 146 Issue: 2 Pages: 295-369
- DOI
  10.1353/ajm.2024.a923236
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Journal Article] Number of solutions to a special type of unit equations in two unknowns, II2024
- Author(s)
  Takafumi Miyazaki, Istvan Pink
- Journal Title
  
  Research in Number Theory
  
  Volume: 10 Issue: 2
- DOI
  10.1007/s40993-024-00524-7
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Journal Article] A purely exponential Diophantine equation in three unknowns2021
- Author(s)
  Miyazaki Takafumi、Sudo Masaki、Terai Nobuhiro
- Journal Title
  
  Periodica Mathematica Hungarica
  
  Volume: 84 Issue: 2 Pages: 287-298
- DOI
  10.1007/s10998-021-00405-x
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20K03553, KAKENHI-PROJECT-18K03247
[Journal Article] Application of cubic residue theory to an exponential equation concerning Eisenstein triples2020
- Author(s)
  Takafumi Miyazaki
- Journal Title
  
  Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  
  Volume: 62(110) Pages: 305-312
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples2019
- Author(s)
  Takafumi Miyazaki
- Journal Title
  
  Tokyo Journal of Mathematics
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] On Terai's exponential equation with two finite integer parameters2019
- Author(s)
  Takafumi Miyazaki
- Journal Title
  
  Notes Number Theory Discrete Mathematics
  
  Volume: 25 Issue: 1 Pages: 84-107
- DOI
  10.7546/nntdm.2019.25.1.84-107
- NAID
  120006861274
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] A study on the exponential Diophantine equation a^x+(a+b)^y=b^z2019
- Author(s)
  Takafumi Miyazaki, Nobuhiro Terai
- Journal Title
  
  Publicationes Mathematicae Debrecen
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] On the Diophantine equation ((c+1)m^2+1)^x+(cm^2-1)^y=(am)^z2018
- Author(s)
  E. Kizildere, T. Miyazaki, G. Gokhan
- Journal Title
  
  Turkish Journal of Mathematics
  
  Volume: 42 Issue: 5 Pages: 2690-2698
- DOI
  10.3906/mat-1803-14
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] On the number of extensions of a Diophantine triple2018
- Author(s)
  Mihai Cipu, Yasutsugu Fujita, Takafumi Miyazaki
- Journal Title
  
  International Journal of Number Theory
  
  Volume: 14 Issue: 03 Pages: 899-917
- DOI
  10.1142/s1793042118500549
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557, KAKENHI-PROJECT-16K05079
[Journal Article] Contributions to some conjectures on a ternary exponential Diophantine equation2018
- Author(s)
  Takafumi Miyazaki
- Journal Title
  
  Acta Arithmetica
  
  Volume: 186.1 Issue: 1 Pages: 1-36
- DOI
  10.4064/aa8656-2-2018
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] The regularity of Diophantine quadruples2017
- Author(s)
  Yasutsugu Fujita, Takafumi Miyazaki
- Journal Title
  
  Transactions of the American Mathematical Society
  
  Volume: 印刷中 Issue: 6 Pages: 3803-3831
- DOI
  10.1090/tran/7069
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-16K17557, KAKENHI-PROJECT-16K05079
[Journal Article] A polynomial-exponential equation related to the Ramanujan-Nagell equation,2017
- Author(s)
  Takafumi Miyazaki
- Journal Title
  
  The Ramanujan Journal
  
  Volume: 印刷中 Issue: 3 Pages: 601-613
- DOI
  10.1007/s11139-016-9878-x
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-16K17557
[Journal Article] On the diophantine equation 1+x^a+z^b=y^n2016
- Author(s)
  Attila Berczes, Lajos Hajdu, Takafumi Miyazaki, Istvan Pink
- Journal Title
  
  Journal of Number Theory and Combinatorics
  
  Volume: 8 Pages: 145-154
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557
[Presentation] Number of solutions to a special type of unit equations in two unknowns III2024
- Author(s)
  Takafumi Miyazaki, Istvan Pink
- Organizer
  Diophantine Analysis and Related Fields 2024
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Number of solutions to a special type of Pillai’s equation2023
- Author(s)
  Takafumi Miyazaki
- Organizer
  25th Central European Number Theory Conference
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Number of solutions to a special type of Pillai’s equation2023
- Author(s)
  Takafumi Miyazaki
- Organizer
  解析的整数論とその周辺（2023年度RIMS共同研究（公開型））
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Number of solutions to a special type of unit equations in two unknowns II2022
- Author(s)
  Takafumi Miyazaki
- Organizer
  Number Theory Conference 2022
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Number of solutions to a special type of unit equations in two unknowns II2022
- Author(s)
  Takafumi Miyazaki
- Organizer
  NUMBER THEORY SEMINAR (Number Theory Research Group University of Debrecen)
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] 三変数の純指数型不定方程式に関するScottの定理について2021
- Author(s)
  宮崎　隆史
- Organizer
  2021大分整数論研究集会
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Number of solutions to some purely exponential Diophantine equation in three unknowns2021
- Author(s)
  Takafumi Miyazaki
- Organizer
  2021年度RIMS共同研究 (公開型) 解析的整数論とその周辺
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] 純指数型不定方程式a^x+b^y=c^zの解の個数について2021
- Author(s)
  宮崎　隆史
- Organizer
  日本数学会2021年度秋季総合分科会
- Data Source
  KAKENHI-PROJECT-20K03553
[Presentation] Application of cubic residue theory to a special type of unit equation concerning Eisenstein triples2019
- Author(s)
  Takafumi Miyazaki
- Organizer
  Diophantine Analysis and Related Fields 2019
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557
[Presentation] Coincidence between two sequences of polynomials arising from Diophantine triples2018
- Author(s)
  Takafumi Miyazaki
- Organizer
  Conference on Diophantine m-tuples and Related Problems II
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557
[Presentation] On Terai’s exponential equation with two finite integer parameters2018
- Author(s)
  Takafumi Miyazaki
- Organizer
  Analytic Number Theory and Related Areas
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557
[Presentation] Extension of Dem’janenko’s classical work on a quadratic Diophantine equation and its applications2017
- Author(s)
  Takafumi Miyazaki
- Organizer
  Diophantine Analysis and Related Fields 2017
- Place of Presentation
  日本大学（東京都・千代田区）
- Year and Date
  2017-01-09
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K17557

Miyazaki Takafumi 宮崎 隆史

Research Projects

Research Products

Effective rational approximation to algebraic irrationals and exponential Diophantine equationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Algebraic and analytic study on exponential equations related to Fermat's equationPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Diophantine problems related to polynomial-exponential equationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Number of solutions to a special type of unit equations in two unknowns2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Number of solutions to a special type of unit equations in two unknowns, II2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] A purely exponential Diophantine equation in three unknowns2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Application of cubic residue theory to an exponential equation concerning Eisenstein triples2020

Author(s)

Journal Title

Data Source

[Journal Article] Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples2019

Author(s)

Journal Title

Data Source

[Journal Article] On Terai's exponential equation with two finite integer parameters2019

Author(s)

Journal Title

DOI

NAID

Data Source

[Journal Article] A study on the exponential Diophantine equation a^x+(a+b)^y=b^z2019

Author(s)

Journal Title

Data Source

[Journal Article] On the Diophantine equation ((c+1)m^2+1)^x+(cm^2-1)^y=(am)^z2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On the number of extensions of a Diophantine triple2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Contributions to some conjectures on a ternary exponential Diophantine equation2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The regularity of Diophantine quadruples2017

Author(s)

Journal Title

DOI

Data Source

[Journal Article] A polynomial-exponential equation related to the Ramanujan-Nagell equation,2017

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On the diophantine equation 1+x^a+z^b=y^n2016

Miyazaki Takafumi 宮崎隆史