MURATA Leo 村田玲音

Researcher Number	30157789
Other IDs
External Links
Affiliation (based on the past Project Information) *help	2000 – 2011: 明治学院大学, 経済学部, 教授 1999: 明治学院大学, 一般教育部, 教授
Review Section/Research Field	Principal Investigator Algebra / Algebra
Keywords	Principal Investigator 剰余位数 / 原始根に関するArtin予想 / 剰余指数 / L(1 / 原始根に関するArtinの予想 / Gray Code / Code理論 / estimate of character sums / Artin's Conjecture on primitive roots / resudual index … More / residual order / 指標和の評価 / 余剰指数 / 余剰位数 / Artin's Conjecture Primitive Roots / the Residual Index / the Residual Order / 2+it,X) / Character Sums / Burgessのbound / Vinogradovの不等式 / 原始根の分布 / Lー関数の特殊値 / 2+it, X) / 指標和 / Sum of digits function / 一般剩余類群 / 一般剰余類群 / Automaton / Sum of diits function / paper-folding sequence / code / Code 理論 / 数論的関数 / 解析的整数論 / Sum of digits関数 / 剩余位数 / 原始根 Less

Arithmetical Functions, Code Theory and Distribution properties of the Residual OrderPrincipal Investigator
- Principal Investigator
  
  MURATA Leo
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji Gakuin University
On the distribution of the residual order/index of the residual class a(mod n) in the residual group with composite moduli.Principal Investigator
- Principal Investigator
  
  MURATA Leo
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji Gakuin University
Analytic study on distribution properties of the residual order and residual index, and on the relation between the distribution and estimates on character sumsPrincipal Investigator
- Principal Investigator
  
  MURATA Leo
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji Gakuin University
An analytic research on "estimates of character sums" and "the distribution property of primitive roots"Principal Investigator
- Principal Investigator
  
  MURA Leo
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji Gakuin University

All 2013 2012 2011 2010 2009 2008 2006 2004 2003 2002 Other

All Journal Article Presentation

[Journal Article] Certain codes related to generalized paper-folding sequences2013
- Author(s)
  Yuichi KAMIYA and Leo MURATA
- Journal Title
  
  Journal de Theorie des Nombres de BORDEAUX
  
  Volume: Vol. 25(to appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] 原始根や剰余位数にまつわる話2013
- Author(s)
  村田玲音
- Journal Title
  
  数学セミナー
  
  Volume: 7月号
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] Certain codes related to generalized paper-folding sequences,2013
- Author(s)
  Yuich KAMIYA et Leo MURATA
- Journal Title
  
  J. de Theorie des Nombres de Bordeaux
  
  Volume: 25
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] Relations among arithmetical functions, automatic sequences and sum of digits functions induced by certain Gray codes2012
- Author(s)
  Yuichi KAMIYA and Leo MURATA
- Journal Title
  
  Journal de Theorie des Nombres de BORDEAUX
  
  Volume: Vol. 24 Pages: 307-337
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] 剰余位数の分布について2012
- Author(s)
  村田玲音
- Journal Title
  
  経済研究(明治学院大学)
  
  Volume: 第145号 Pages: 55-66
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes2012
- Author(s)
  Yuichi KAMIYA et Leo MURATA
- Journal Title
  
  J. de Theorie des Nombres de Bordeaux
  
  Volume: 24 Pages: 307-337
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] On the average of some q-additive functions2008
- Author(s)
  Leo Murata, Yuichi Kamiya
- Journal Title
  
  Annales Univ. Sci. Budapest., Sect. Comp. Vol. 29
  
  Pages: 39-63
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On the average of some q-additive functions.2008
- Author(s)
  Leo Murata and Yuichi Kamiya
- Journal Title
  
  Annales Univ. Sci. Budapest., Sect, Comp. 29
  
  Pages: 39-63
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On a distribution property of the residual order of a (mod p), part III2006
- Author(s)
  L. Murata, K. Chinen
- Journal Title
  
  J. of Math. Soc. Japan Vol. 58-3
  
  Pages: 693-720
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On a distribution property of the residual order of a(mod p) IV.2006
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Number Theory : Tradition and Modernization (Ed.by W.Zhang, Y.Tanigawa)(Springer Science + Business Media, Inc.)
  
  Pages: 11-22
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a (mod p) III2006
- Author(s)
  Koji Chinen and Leo Murata
- Journal Title
  
  J. of Mathematical Society of Japan
  
  Volume: Vol. 58 Pages: 693-720
- NAID
  10018381051
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] On a distribution property of the residual order of a(mod p) III.2006
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Journal of Math.Soc.Japan Vol.58-3
  
  Pages: 693-720
- NAID
  10018381051
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] ON A DISTRIBUTION PROPERTY OF THE RESIDUAL ORDER OF a(mod p) - IV2006
- Author(s)
  Leo Murata (with K. Chinen)
- Journal Title
  
  Number Theory : Tradition and Modernization (Edited by Y. Tanigawa, W. Zhang) (Springer Science)
  
  Pages: 11-22
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On a distribution property of the residual order of a(mod p) - III2006
- Author(s)
  Leo Murata (with K. Chinen)
- Journal Title
  
  J. of Math. Soc. Japan 58-3
  
  Pages: 693-720
- NAID
  10018381051
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On a distribution property of the residual order of a (mod p), part IV,2006
- Author(s)
  L. Murata, K. Chinen
- Journal Title
  
  "Number Theory: Tradition and Modernization", Edited by Y. Tanigawa and W. ZhangSpringer Science
  
  Pages: 11-22
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540054
[Journal Article] On a distribution property of the residual order of a (mod p) IV, Number Theory, Tradition and Modernization2006
- Author(s)
  Koji Chinen and Leo Murata
- Journal Title
  
  Springer Science
  
  Pages: 11-22
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] On a distribution property of the residual order of a(mod p) IV2006
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  論文集 : "Number Theory : Tradition and Modernization"(Ed. by W. Zhang, Y. Tanigawa)
  
  Pages: 11-22
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p) III2006
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  Journal of Math. Soc. Japan 58
  
  Pages: 693-720
- NAID
  10018381051
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of a residual order of a(mod p) II.2004
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Proc.of Japan Acad. Vol.80
  
  Pages: 182-186
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p) II2004
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  Journal of Number Theory 105
  
  Pages: 82-100
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On the largest prime factor of a Mersenne number2004
- Author(s)
  Leo Murata, Carol Pomerance
- Journal Title
  
  CRM Proceedings & Lecture Notes 36
  
  Pages: 209-218
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On the largest prime factor of a Mersenne number.2004
- Author(s)
  Leo Murata (with Carl Pomerance)
- Journal Title
  
  Center de Recherches Mathematiques, CRM Prceedings and Lecture Notes Volume 36
  
  Pages: 209-218
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of a residual order of a (mod p), (2)2004
- Author(s)
  Leo Murata, K.Chinen
- Journal Title
  
  Proceedings of the Japan Academy 80
  
  Pages: 182-186
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a (mod p)2004
- Author(s)
  Koji Chinen and Leo Murata
- Journal Title
  
  J. of Number Theory
  
  Volume: Vol. 105 Pages: 60-81
- NAID
  40005723985
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] On the largest prime factor of a Mersenne number2004
- Author(s)
  Leo Murata, C. Pomerance
- Journal Title
  
  Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes 36
  
  Pages: 209-218
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of a residual order of a(mod p) II2004
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  Proc. of Japan Acad. 80
  
  Pages: 182-186
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p) IV2004
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  京都大学数理解析研究所講究録 1384
  
  Pages: 169-174
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a (mod p) II2004
- Author(s)
  Leo Murata and Koji Chinen
- Journal Title
  
  J. of Number Theory
  
  Volume: Vol. 105 Pages: 82-100
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540027
[Journal Article] On a distribution property of the residual order of a(mod p) II.2004
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Journal of Number Theory vol.105
  
  Pages: 82-100
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p)2004
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  Journal of Number Theory 105
  
  Pages: 60-81
- NAID
  40005723985
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a (mod p). IV2004
- Author(s)
  Leo Murata, K.Chinen
- Journal Title
  
  京都大学数理解析研究所講究録 1384
  
  Pages: 169-174
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p).2004
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Journal of Number Theory Vol.105
  
  Pages: 60-81
- NAID
  40005723985
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a property of the multiplicative order of a(mod p).2004
- Author(s)
  Leo Murata
- Journal Title
  
  Proceedings of the 2003 Workshop on Cryptography and Related Mathematics, Chuo University
  
  Pages: 199-207
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a property of the multiplicative order of a(mod p)2004
- Author(s)
  Leo Murata
- Journal Title
  
  Proceedings of the 2003 Workshop on Cryptography and Related Mathematics
  
  Pages: 199-207
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a(mod p) III2003
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  京都大学数理解析研究所講究録 1319
  
  Pages: 139-147
- NAID
  10018381051
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of a residual order of a(mod p)2003
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  Proc. of Japan Acad. 79
  
  Pages: 28-32
- NAID
  40005723985
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of a residual order of a(mod p).2003
- Author(s)
  Leo Murata (with Koji Chinen)
- Journal Title
  
  Proc.of Japan Acad. Vol.79
  
  Pages: 28-32
- NAID
  40005723985
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] a (mod p)の剰余位数の分布について II2002
- Author(s)
  Leo Murata, K. Chinen
- Journal Title
  
  京都大学数理解析研究所講究録 1274
  
  Pages: 62-69
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] On a distribution property of the residual order of a (mod p)-III
- Author(s)
  Leo Murata (with K.Chinen)
- Journal Title
  
  Journal of the Mathematical Society of Japan to appear
- NAID
  10018381051
- Data Source
  KAKENHI-PROJECT-14540048
[Journal Article] ON A DISTRIBUTION PROPERTY OF THE RESUDUAL ORDER OF a (mod p)-IV
- Author(s)
  Leo Murata (with K.Chinen)
- Journal Title
  
  Number Theory. Tradition and Modernization(Edited by Y.Tanigawa and W.Zhang)(Springer Veerlag) to appear
- Data Source
  KAKENHI-PROJECT-14540048
[Presentation] (Z/pZ)^*や(Z/pgZ)^*での剰余指数・剰余位数の分布について2011
- Author(s)
  村田玲音
- Organizer
  日本数学会
- Place of Presentation
  信州大学(春の年会(大震災のため実際の発表は秋に延期))(特別講演)
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] On a distribution property of the multiplicative order of a(mod p) and a(mod pq)2010
- Author(s)
  Leo Murata
- Organizer
  Colorado Kempner Colloquium
- Place of Presentation
  Colorado Univ.in Boulder, Colorado, USA(アメリカ)
- Year and Date
  2010-09-30
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] On a distribution property of the multiplicative order of a(mod p) and a(mod pq)2010
- Author(s)
  村田玲音
- Organizer
  Kempner Colloquium (Colorado University)
- Place of Presentation
  米国・コロラド大学・ボウルダー校
- Year and Date
  2010-09-30
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] (Z/pZ)*や(Z/pqZ)*での剰余位数・剰余指数の分布について2010
- Author(s)
  村田玲音
- Organizer
  日本数学会、2011年春の学会(特別講演)
- Place of Presentation
  信州大学
- Year and Date
  2010-10-01
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] A relation between simple arithmetical functions and Code systems2009
- Author(s)
  村田玲音(with 神谷諭一)
- Organizer
  Zeta Function Days at Seoul
- Place of Presentation
  韓国・ソウル・延世大学
- Year and Date
  2009-09-02
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] 数論的関数と Code システムのある関係について2009
- Author(s)
  村田玲音(with 神谷諭一)
- Organizer
  AC2009「第8回代数学と計算シンポジウム」
- Place of Presentation
  首都大学東京
- Year and Date
  2009-12-03
- Data Source
  KAKENHI-PROJECT-21540027
[Presentation] Some q-additive functions and related topics2008
- Author(s)
  村田玲音
- Organizer
  The 5^<th> Japan-China Seminar on Number Theory
- Place of Presentation
  近畿大学・理工学部
- Year and Date
  2008-08-28
- Data Source
  KAKENHI-PROJECT-18540054
[Presentation] On a property of the multiplicative order of a(mod p)2006
- Author(s)
  村田玲音
- Organizer
  The 4^<th> Japan-China Seminar on Number Theory
- Place of Presentation
  中国・山東大学
- Year and Date
  2006-09-03
- Data Source
  KAKENHI-PROJECT-18540054

1. KITAOKA Yoshiyuki (40022686)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
2. OKAZAKI Ryutarou (20268113)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
3. CHINEN Koji (30419486)

# of Collaborated Projects: 2 results

# of Collaborated Products: 8 results
4. KAMIYA Yuichi (90553412)

# of Collaborated Projects: 1 results

# of Collaborated Products: 6 results

MURATA Leo 村田 玲音

Research Projects

Research Products

Co-Researchers

Arithmetical Functions, Code Theory and Distribution properties of the Residual OrderPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

On the distribution of the residual order/index of the residual class a(mod n) in the residual group with composite moduli.Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Analytic study on distribution properties of the residual order and residual index, and on the relation between the distribution and estimates on character sumsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

An analytic research on "estimates of character sums" and "the distribution property of primitive roots"Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Certain codes related to generalized paper-folding sequences2013

Author(s)

Journal Title

Data Source

[Journal Article] 原始根や剰余位数にまつわる話2013

Author(s)

Journal Title

Data Source

[Journal Article] Certain codes related to generalized paper-folding sequences,2013

Author(s)

Journal Title

Data Source

[Journal Article] Relations among arithmetical functions, automatic sequences and sum of digits functions induced by certain Gray codes2012

Author(s)

Journal Title

Data Source

[Journal Article] 剰余位数の分布について2012

Author(s)

Journal Title

Data Source

[Journal Article] Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes2012

Author(s)

Journal Title

Data Source

[Journal Article] On the average of some q-additive functions2008

Author(s)

Journal Title

Data Source

[Journal Article] On the average of some q-additive functions.2008

Author(s)

Journal Title

Data Source

[Journal Article] On a distribution property of the residual order of a (mod p), part III2006

Author(s)

Journal Title

Data Source

[Journal Article] On a distribution property of the residual order of a(mod p) IV.2006

Author(s)

Journal Title

Description

Data Source

[Journal Article] On a distribution property of the residual order of a (mod p) III2006

Author(s)

Journal Title

NAID

Data Source

[Journal Article] On a distribution property of the residual order of a(mod p) III.2006

Author(s)

Journal Title

NAID

Description

Data Source

MURATA Leo 村田玲音