TANAKA Takaaki 田中孝明

Researcher Number	60306850
Other IDs
Affiliation (Current)	2019 : 慶應義塾大学, 理工学部(矢上), 准教授
Affiliation (based on the past Project Information) *help	2015 – 2017 : 慶應義塾大学, 理工学部(矢上), 准教授 2014 – 2015 : 慶應義塾大学, 理工学部, 准教授 2013 : 慶応義塾大学, 理工学部, 講師 2010 – 2013 : 慶應義塾大学, 理工学部, 講師 2010 – 2012 : 慶應義塾大学, 理工学部, 専任講師 2007 – 2009 : Keio University, Faculty of Science and Technology, Research Associate 2005 – 2006 : 慶應義塾大学, 理工学部, 助手
Review Section/Research Field	Principal Investigator Algebra Except Principal Investigator Algebra / General mathematics (including Probability theory/Statistical mathematics)
Keywords	Principal Investigator Mahler関数 / 超越数 / フィボナッチ数列 / p進数 / 代数的独立性 / 正標数 / Hecke-Mahler級数 / 整関数 / Mahler 関数 / 代数的独立 … More Except Principal Investigator 国際研究者交流 / 整数論 / 岩澤理論 / Selmer群 / 岩澤主予想 / セルマー群 / イデアル類群 / Rankin-Selberg / 連分数 / Fittingイデアル / 楕円曲線 / 実解析的Eisenstein級数 / 数論 / 半整数重さ / 岩澤加群 / 正規化メリン変換 / Stark予想 / ドイツ：イギリス / zonal polynomial / 合流型超幾何積分 / 退化主系列表現 / Leaping convergents / Eisenstein seeries / Rankin-Selber / Maassリフティング / Selmer 群 / p進L関数 / フランス:オランダ:イスラエル / Zonal多項式 / 非アルキメデス数体 / イギリス：ドイツ：中国：ベトナム / ゼータ関数 / Degenerate principal series / Kolyvagin系 / 測度論的数論 / 合流型超幾何函数 / イギリス / Mellin transform / Tate Shafarevich群 / 実解析的Siegel保型形式 / カナダ:中国:アメリカ / Koecher-Maass級数 / 一般型メリン変換 / 国際情報交換 / 測度論敵数論 / メリン変換 / 退化Whittaker模型 / Stickelberger元 / confluent hypergeometric function / 組合せ論 / 線形関係式 / ドイツ:韓国 / 組み合わせ論 / Ge enbauer多項式 / Zuckerman導来函手加群 / Rankin-Selberg L函数 / イタリア:フランス:オランダ / Euler系 / 有理点 / 代数学 / 留数形式 / アイゼンシュタイン級数 / イギリス:アメリカ:韓国 / 斉藤・黒川保型形式 / 実解析的保型形式 / Fitting イデアル Less

非アルキメデス付値体における完全代数的独立性Principal InvestigatorOngoing
- Principal Investigator
  
  田中孝明
- Project Period (FY)
  2015 – 2018
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Keio University
岩澤理論の発展と展開Ongoing
- Principal Investigator
  
  栗原将人
- Project Period (FY)
  2013 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Algebra
- Research Institution
  Keio University
Analytic, Algebraic and Combinatorial studies on continued fractions
- Principal Investigator
  
  KOMATSU Takao
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hirosaki University
Structural analysis of transcendental numbers through the values of Mahler functionsPrincipal Investigator
- Principal Investigator
  
  TANAKA Takaaki
- Project Period (FY)
  2010 – 2012
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Keio University
New development of Iwasawa theory and its applications
- Principal Investigator
  
  KURIHARA Masato
- Project Period (FY)
  2009 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Keio University
Ergodic theory and metric number theory
- Principal Investigator
  
  NAKADA Hitoshi
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Keio University
Transcendence and algebraic independence of Mahler functions over p-adic number fields and function fields and its applicationsPrincipal Investigator
- Principal Investigator
  
  TANAKA Takaaki
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Keio University
Refined Iwasawa theory and the zeta functions
- Principal Investigator
  
  KURIHARA Masato
- Project Period (FY)
  2005 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Keio University
Arithmetic of cohomological automorphic representations of orthogonal groups and theta series for indefinite quadratic forms
- Principal Investigator
  
  MIYAZAKI Takuya
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Keio University

All 2018 2017 2016 2013 2012 2011 2010 2009 2008 2006 2005 Other

All Journal Article Presentation

[Journal Article] Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field2018
- Author(s)
  Goto Akinari、Tanaka Taka-aki
- Journal Title
  
  Journal of Number Theory
  
  Volume : 184 Pages : 384-410
- DOI
  10.1016/j.jnt.2017.08.026
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04792
[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013
- Author(s)
  T. Kurosawa, Y. Tachiya, and T. Tanaka
- Journal Title
  
  Annales Mathematicae et Informaticae
  
  Volume : 41
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013
- Author(s)
  T. Kurosawa, Y. Tachiya, and T. Tanaka
- Journal Title
  
  Ann. Math. Inform
  
  Volume : 41(掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013
- Author(s)
  Takeshi Kurosawa, Yohei Tachiya and Taka-aki Tanaka
- Journal Title
  
  Annales Mathematicae et Informaticae
  
  Volume : 41 Pages : 107-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25247002
[Journal Article] Algebraic independence properties related to certain infinite products2012
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  AIP Conference Proceedings
  
  Volume : 1385 Pages : 116-123
- DOI
  10.1063/1.3630047
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Algebraic independence properties related to certain infinite products, AIP Conference Proceedings 1385,Diophantine Analysis and Related Fields 20112012
- Author(s)
  T. Tanaka
- Journal Title
  
  American Institute of Physics
  
  Pages : 116-123
- URL
  http://dx.doi.org/10.1063/1.3630047
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Algebraic independence of infinite products generated by Fibonacci numbers2010
- Author(s)
  Y.Tachiya, T.Tanaka, T.Kurosawa
- Journal Title
  
  Tsukuba Journal of Mathematics
  
  Volume : 34 Pages : 255-264
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Algebraic independence of infinite products generated by Fibonacci numbers2010
- Author(s)
  T. Kurosawa, Y. Tachiya, and T. Tanaka
- Journal Title
  
  Tsukuba J. Math
  
  Volume : 34 Pages : 255-264
- URL
  http://projecteuclid.org/euclid.tkbjm/1302268248
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22740023
[Journal Article] Mahler-Manin予想の解決とMahler関数-Mahlerの方法による超越性・代数的独立性の証明へのイントロダクション-2009
- Author(s)
  田中孝明
- Journal Title
  
  整数論サマースクール報告集 (掲載確定)
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences2009
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Journal of Number Theory 129
  
  Pages : 3081-3093
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21340012
[Journal Article] Remarkable algebraic independence property of certain series related to continued fractions2008
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Diophantine analysis and related fields-DARF 2007/2008, AIP Conf. Proc 976, Melville, NY
  
  Pages : 190-204
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Remarkable algebraic independence property of certain series related to continued fractions2008
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Diophantine analysis and related fields---DARF 2007/2008, AIP Conf. Proc 976
  
  Pages : 190-204
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Remarkable algebraic cindependence property of certain series related to continued fractions, AIP Conference Proceedings 976, Diophantine Analysis and Related Fields 2007/20082008
- Author(s)
  T. Tanaka
- Journal Title
  
  American Institute of Physics
  
  Pages : 190-204
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Mahler-Manin予想の解決とMahler関数-Mahlerの方法による超越性・代数的独立性の証明へのイントロダクションー2008
- Author(s)
  田中孝明
- Journal Title
  
  第14回整数論サマースクール報告集
  
  Pages : 44-66
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Remarkable algebraic independence property of certain series related to continued fractions2008
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  AIP Conference Proceedings 976
  
  Pages : 190-204
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic independence of modified reciprocal sums of products of Fibonacci numbers2006
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Tsukuba Journal Math. Vol. 30 No. 2
  
  Pages : 345-361
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Algebraic independence of a certain series and its subseries with subscripts in a geometric progression, Seminar on Math. Sci. No. 35, Diophantine Analysis and Related Fields 20062006
- Author(s)
  T. Tanaka
- Journal Title
  
  Keio Univ
  
  Pages : 175-185
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic independence of the values of certain functions at distinct algebraic points,数理解析研究所講究録1511,2006
- Author(s)
  田中孝明
- Journal Title
  
  解析的整数論との周辺(Analytic Number Theory and Surrounding Areas)
  
  Pages : 10-18
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic indep-endence of modified reciprocal sums of products of Fibonacci numbers2006
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Tsukuba J. Math 30
  
  Pages : 345-361
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Aalgebraic independence of a certain series and its subseries with subscripts in a geometric progression2006
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Seminar on Mathematical Sciences (Keio Univ.) 35
  
  Pages : 175-185
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic independence of the values of certain functions at distinct algebraic points2006
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  数理解析研究所講究録 1511
  
  Pages : 10-18
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic independence of modified reciprocal sums of products of Fibonacci numbers2006
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Tsukuba Journal of Mathematics 30
  
  Pages : 345-361
- Data Source
  KAKENHI-PROJECT-18740017
[Journal Article] Algebraic indep- endence of the values of power series2005
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Lambert series, and infinite products generated by linear recurrences, Osaka J. Math 42
  
  Pages : 487-497
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences2005
- Author(s)
  Tanaka Taka-aki
- Journal Title
  
  Osaka Journal of Mathematics 42
  
  Pages : 487-497
- Data Source
  KAKENHI-PROJECT-17340010
[Journal Article] Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences2005
- Author(s)
  Taka-aki Tanaka
- Journal Title
  
  Osaka Journal of Mathematics 42・2
  
  Pages : 487-497
- Data Source
  KAKENHI-PROJECT-17540038
[Journal Article] Mahler-Manin予想の解決とMahler関数
- Author(s)
  田中孝明
- Journal Title
  
  第14回整数論サマースクール報告集 (掲載確定)
- Data Source
  KAKENHI-PROJECT-18740017
[Presentation] On the functions having `perfect' algebraic independence property at algebraic numbers2017
- Author(s)
  Taka-aki Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2017
- Place of Presentation
  日本大学（東京都・千代田区）
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04792
[Presentation] 有限個の素数pに対するQpとRの`共通部分'に属する超越数から成る代数的独立な無限集合について2016
- Author(s)
  田中孝明, 中島ミホ
- Organizer
  日本数学会年会
- Place of Presentation
  筑波大学（茨城県・つくば市）
- Year and Date
  2016-03-18
- Data Source
  KAKENHI-PROJECT-15K04792
[Presentation] Algebraic independence of the values of Mahler functions with 'negative' transformations2012
- Author(s)
  Taka-aki Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2012
- Place of Presentation
  新潟大学
- Year and Date
  2012-01-10
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence of the values of certain infinite products and their derivatives related to Fibonacci and Lucas numbers2012
- Author(s)
  T. Tanaka
- Organizer
  RIMS 研究集会「解析的整数論とその周辺近似と漸近的手法を通して見た数論」
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2012-10-30
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence of the values of Mahler functions with 'negative'transformations2012
- Author(s)
  T. Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2012
- Place of Presentation
  新潟大学
- Year and Date
  2012-01-10
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence properties related to certain infinite products and Lambert series2011
- Author(s)
  T. Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2011
- Place of Presentation
  成蹊大学
- Year and Date
  2011-03-03
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence properties related to certain infinite products and Lambert series2011
- Author(s)
  T.Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2011
- Place of Presentation
  成蹊大学理工学部
- Year and Date
  2011-03-03
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence of the values of a certain entire function defined by the infinite product2010
- Author(s)
  T.Tanaka
- Organizer
  解析数論-複素関数の値の分布と性質を通して-
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2010-10-08
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence of the values of a certain entire function defined by the infinite product2010
- Author(s)
  T. Tanaka
- Organizer
  RIMS 研究集会「解析数論複素関数の値の分布と性質を通して」
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2010-10-08
- Data Source
  KAKENHI-PROJECT-22740023
[Presentation] Algebraic independence of the values of a certain entire function defined by the infinite product2010
- Author(s)
  Taka-aki Tanaka
- Organizer
  解析数論 -複素関数の値の分布と性質を通して
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2010-10-08
- Data Source
  KAKENHI-PROJECT-21340012
[Presentation] Algebraic independence of certain series involving continued fractions and generated by linear recurrences2008
- Author(s)
  T. Tanaka
- Organizer
  解析的整数論の新しい展開(New Aspects of Analytic Number Theory)
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2008-10-27
- Data Source
  KAKENHI-PROJECT-18740017
[Presentation] Remarkable algebraic independence property of certain series related to continued fractions2008
- Author(s)
  T. Tanaka
- Organizer
  Diophantine Analysis and Related Fields 2008
- Place of Presentation
  同志社大学
- Year and Date
  2008-03-06
- Data Source
  KAKENHI-PROJECT-18740017
[Presentation] Algebraic independence of certain series involving continued fractions and generated by linear recurrences2008
- Author(s)
  Takaaki Tanaka
- Organizer
  解析的整数論の新しい展開
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2008-10-27
- Data Source
  KAKENHI-PROJECT-18740017
[Presentation] Mahler-Manin予想の解決とMahler関数2006
- Author(s)
  田中孝明
- Organizer
  第14回整数論サマースクール
- Place of Presentation
  静岡県伊豆の国市
- Year and Date
  2006-08-15
- Data Source
  KAKENHI-PROJECT-18740017
[Presentation] Algebraic independence of the values of certain infinite products and their derivatives related to Fibonacci and Lucas numbers
- Author(s)
  T. Tanaka
- Organizer
  解析的整数論とその周辺 ―近似と漸近的手法を通して見た数論
- Place of Presentation
  京都大学数理解析研究所
- Data Source
  KAKENHI-PROJECT-22740023

1. MATSUNO Kazuo (40332936)

# of Collaborated Projects : 4results

# of Collaborated Products : 0results
2. HACHIMORI Yoshitaka (50433743)

# of Collaborated Projects : 4results

# of Collaborated Products : 0results
3. KURIHARA Masato (40211221)

# of Collaborated Projects : 3results

# of Collaborated Products : 0results
4. MIYAZAKI Takuya (10301409)

# of Collaborated Projects : 3results

# of Collaborated Products : 0results
5. OTA Katsuhiro (40213722)

# of Collaborated Projects : 2results

# of Collaborated Products : 0results
6. BANNAI Kenichi (90343201)

# of Collaborated Projects : 2results

# of Collaborated Products : 0results
7. 藤井俊 (20386618)

# of Collaborated Projects : 2results

# of Collaborated Products : 0results
8. NATSUI Rie (60398633)

# of Collaborated Projects : 2results

# of Collaborated Products : 0results
9. KOBAYASHI Shinichi (80362226)

# of Collaborated Projects : 2results

# of Collaborated Products : 0results
10. SHIOKAWA Iekata (00015835)

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11. AOKI Miho (10381451)

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12. 落合理 (90372606)

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13. 加藤和也 (90111450)

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14. NAKADA Hitoshi (40118980)

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15. MAEJIMA Makoto (90051846)

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16. TAMURA Yozo (50171905)

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17. ATSUJI Atsushi (00221044)

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18. YASUDA Kumi (40284484)

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19. ISHII Ippei (90051929)

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20. KATSURA Takeshi (50513298)

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21. MIURA Takashi (60631934)

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22. KOMATSU Takao (70300556)

# of Collaborated Projects : 1results

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23. MUNEMASA Akihiro (50219862)

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24. AKIYAMA Shigeki (60212445)

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25. ODA Yoshiaki (90325043)

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26. 深谷太香子 (20365464)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results

TANAKA Takaaki 田中 孝明

Research Projects

Research Products

Co-Researchers

非アルキメデス付値体における完全代数的独立性Principal InvestigatorOngoing

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

岩澤理論の発展と展開Ongoing

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Analytic, Algebraic and Combinatorial studies on continued fractions

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Structural analysis of transcendental numbers through the values of Mahler functionsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

New development of Iwasawa theory and its applications

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Ergodic theory and metric number theory

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Transcendence and algebraic independence of Mahler functions over p-adic number fields and function fields and its applicationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Refined Iwasawa theory and the zeta functions

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Arithmetic of cohomological automorphic representations of orthogonal groups and theta series for indefinite quadratic forms

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013

Author(s)

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Data Source

[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013

Author(s)

Journal Title

Data Source

[Journal Article] Algebraic relations with the infinite products generated by Fibonacci numbers2013

Author(s)

Journal Title

Data Source

[Journal Article] Algebraic independence properties related to certain infinite products2012

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Data Source

TANAKA Takaaki 田中孝明