TANAKA Takaaki 田中孝明

Researcher Number	60306850
Other IDs
Affiliation (Current)	2022: 慶應義塾大学, 理工学部(矢上), 准教授
Affiliation (based on the past Project Information) *help	2015 – 2020: 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 / Basic Section 11010:Algebra-related Except Principal Investigator Algebra / General mathematics (including Probability theory/Statistical mathematics)
Keywords	Principal Investigator 代数的独立性 / Mahler関数 / 超越数 / p進数 / 線形回帰数列 / フィボナッチ数列 / 連分数 / P進数 / 多変数関数 / 線形回帰整数列 … More Except Principal Investigator 整数論 / 国際研究者交流 / 岩澤理論 / 楕円曲線 / 岩澤主予想 / Fittingイデアル / 連分数 / セルマー群 / イデアル類群 / Selmer群 / Rankin-Selberg / Kolyvagin系 / ドイツ:韓国 / Euler系 / Stickelberger元 / p進L関数 / 有理点 / 非アルキメデス数体 / 測度論的数論 / 測度論敵数論 / フランス:オランダ:イスラエル / 国際情報交換 / イタリア:フランス:オランダ / Tate Shafarevich群 / Selmer 群 / Fitting イデアル / ドイツ：イギリス / イギリス / イギリス:アメリカ:韓国 / カナダ:中国:アメリカ / 数論 / 代数学 / 組み合わせ論 / 組合せ論 / 線形関係式 / Leaping convergents / Stark予想 / 同変岩澤主予想 / 同変玉河数予想 / ゼータ関数 / 岩澤加群 / イギリス：ドイツ：中国：ベトナム / 退化主系列表現 / アイゼンシュタイン級数 / Zonal多項式 / 合流型超幾何積分 / メリン変換 / Ge enbauer多項式 / 一般型メリン変換 / Rankin-Selber / 斉藤・黒川保型形式 / 実解析的保型形式 / 正規化メリン変換 / 半整数重さ / 留数形式 / 実解析的Siegel保型形式 / 実解析的Eisenstein級数 / Zuckerman導来函手加群 / 合流型超幾何函数 / 退化Whittaker模型 / Maassリフティング / Koecher-Maass級数 / Rankin-Selberg L函数 / Degenerate principal series / Eisenstein seeries / zonal polynomial / confluent hypergeometric function / Mellin transform Less

完全代数的独立性の拡張と高次元化Principal Investigator
- Principal Investigator
  
  田中孝明
- Project Period (FY)
  2020 – 2023
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Keio University
Perfect algebraic independence properties over non-Archimedean valuation fieldsPrincipal Investigator
- Principal Investigator
  
  Tanaka Taka-aki
- Project Period (FY)
  2015 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Keio University
Development of Iwasawsa theory
- Principal Investigator
  
  Kurihara Masato
- 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 2019 2018 2017 2016 2013 2012 2011 2010 2009 2008 2006 2005 Other

All Journal Article Presentation

[Journal Article] Algebraic independence of the values of a certain map defined on the set of orbits of the action of Klein four-group2019
- Author(s)
  田中孝明
- Journal Title
  
  数理解析研究所講究録
  
  Volume: 2131 Pages: 177-187
- NAID
  120006888073
- Open Access
- Data Source
  KAKENHI-PROJECT-15K04792
[Journal Article] Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers2018
- Author(s)
  Tanaka Taka-aki、Tanuma Yusuke
- Journal Title
  
  International Journal of Number Theory
  
  Volume: 14 Pages: 2369-2384
- DOI
  10.1142/s1793042118501440
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K04792
[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
- NAID
  120006309490
- 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
- NAID
  120006309490
- 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
- NAID
  120005366087
- 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
- NAID
  120005366087
- 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
- NAID
  120004845247
- 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
- NAID
  120004845247
- 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] Algebraic independence of the values of a certain map defined on the set of orbits of the action of Klein four-group2018
- Author(s)
  Tanaka Taka-aki
- Organizer
  解析的整数論とその周辺
- Data Source
  KAKENHI-PROJECT-15K04792
[Presentation] Algebraic independence properties of a certain map defined on the set of orbits of the action of Klein four-group2018
- Author(s)
  Tanaka Taka-aki
- Organizer
  Keio-Yonsei Number Theory Workshop
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04792
[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 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: 4 results

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

# of Collaborated Projects: 4 results

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

# of Collaborated Projects: 3 results

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

# of Collaborated Projects: 3 results

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

# of Collaborated Projects: 2 results

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

# of Collaborated Projects: 2 results

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

# of Collaborated Projects: 2 results

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8. NATSUI Rie (60398633)

# of Collaborated Projects: 2 results

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9. KOBAYASHI Shinichi (80362226)

# of Collaborated Projects: 2 results

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10. SHIOKAWA Iekata (00015835)

# of Collaborated Projects: 1 results

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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)

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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)

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TANAKA Takaaki 田中 孝明

Research Projects

Research Products

Co-Researchers

完全代数的独立性の拡張と高次元化Principal Investigator

Principal Investigator

Project Period (FY)

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Perfect algebraic independence properties over non-Archimedean valuation fieldsPrincipal Investigator

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Development of Iwasawsa theory

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Analytic, Algebraic and Combinatorial studies on continued fractions

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

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New development of Iwasawa theory and its applications

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Ergodic theory and metric number theory

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

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Refined Iwasawa theory and the zeta functions

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

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[Journal Article] Algebraic independence of the values of a certain map defined on the set of orbits of the action of Klein four-group2019

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[Journal Article] Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers2018

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[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

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

TANAKA Takaaki 田中孝明