2001 Fiscal Year Annual Research Report

数論アルゴリズムの研究と数論システムの開発

Research Project

Project/Area Number	13440013
Research Institution	Tokyo Metropolitan University
Principal Investigator	中村憲東京都立大学, 理学研究科, 教授 (80110849)
Co-Investigator(Kenkyū-buntansha)	横山和弘九州大学, 理学研究科, 教授 (30333454) 岡本龍明 NTT, PF研, フェロー倉田俊彦東京都立大学, 理学研究科, 助手 (40311899) 長尾孝一関東学院大学, 工学部, 講師 (00308321) 木田雅成電気通信大学, 電気通信学部, 助教授 (20272057)
Keywords	計算機実験 / 数論アルゴリズム / 数論システム / SIMATH / 暗号理論 / 楕円曲線暗号 / 国際研究者交流 / 多国籍
Research Abstract	アルゴリズムの解析や計算機実験による,加法鎖のScholz予想の部分的検証など,雑誌論文にある様な数論アルゴリズムに関する成果を引続きあげた. 日本応用数理学会「数論アルゴリズムとその応用」研究部会(JANT)研究集会(第4同-第6回)を2001年4月27日,7月28日,2002年1月27日に毎回約50名の参加者で開催し,その経過を http://ntw.e-one.uec.ac.jp/jant/ で公表した.第4回「代数学と計算」研究集会を2001年11月5日-9日に143名の参加で開催し,報告集 ftp://tnt.math.metro-u.ac.jp/pub/ac01/ を電子出版した. これらを通じて基本的な数論アルゴリズムの研究を深め,海外の従来のシステムの経験の調査・研究をしてきた. 数論システムの開発に関しては,当初は独自に,システムを設計する予定であったが,ドイツのザールランド大学チームにより1980年代から開発・運用されてきた,数論汎用数式処理システムSIMATHを2002年1月から引継いで運用を開始した.ホームページは http://simath.info/ である.これは楕円曲線の計算を得意とするシステムであり,暗号理論,とりわけ楕円曲線暗号の研究の為の汎用数論システムとして期待される.そこで今後は,これを核にして数論システムの開発を進める事となる.

Research Products
(20 results)

All Other

All Publications (20 results)

[Publications] H.M.Bahig, H.El-Zahar, K.Nakamura: "Some results for some conjectures in addition chains"Combinatrics, Computability and Logic (DMTCS'01). 47-54 (2001)
[Publications] H.M.Bahig, K.Nakamula: "Some properties of nonstar steps in addition chains and new cases where the Scholz conjecture is true"J.Algorithms. (2002)
[Publications] T.Kurata: "Intersection and singleton type assignment characterizing finite Bohm-trees"Information and Computation.
[Publications] H.Ishihara, T.Kurata: "Completeness of intersection and union type assignment systems for call-by-value λ-models"Theoretical Computer Science. 272. 197-221 (2002)
[Publications] M.Kida: "Nonexistence of elliptic curves having good reduction everywhere over certain quadratic fields"Arch.Math.(Basel). 76. 436-440 (2001)
[Publications] M.Kida: "Good reduction of elliptic curves over imaginary quadratic fields"Journal de Theorie de Nombres de Bordeaux. 13. 201-209 (2001)
[Publications] M.Kida: "Computing elliptic curves having good reduction everywhere over quadratic fields"Tokyo J.Math.. 24. 545-558 (2001)
[Publications] T.Izu, J.Kogure, M.Noro, K.Yokoyama: "Order counting of elliptic curves defined over finite fields of characteristic 2"Electorinics and Communications in Japan Part III, -Fundamental Electoric Science. 85・1. 62-70 (2002)
[Publications] M.Noro, K.Yokoyama: "Yet another practical implementation of polynomial factorization over finite finite fields"ISSAC 2002.
[Publications] K.Yamamura: "Maximal unramified extensions of imaginary quadratic number fields of small conductors II"Journal de Theorie des Nombres de Bordeaux. 13・2. (2001)
[Publications] T.Fukuda, K.Komatsu: "On Iwasawa λ_3-invariants of cyclic cubic fields of prime conductor"Math.Comp.. 70・236. 1707-1712 (2001)
[Publications] T.Fukuda, K.Komatsu: "An application of Siegel modular functions to Kronecker's limit formula"LNCS. (2002)
[Publications] H.Srivastava, H.Tsumura: "Certain classes of rapidly convergent series representations for L(2n, x) and L(2n+1, x)"Acta Arithmetica. 100. 195-201 (2001)
[Publications] K.Kozuka, H.Tsumura: "On some modules attached to the Lubin-Tate formal groups"Tokyo J.Math.. 23. 442-465 (2001)
[Publications] H.Tsumura: "On modification of the q-L-series and its applications"Nagoya Math.J.. 164. 185-197 (2001)
[Publications] H.Tsumura: "On some combinatorial relations for Tohnheim's double series"Acta Arithmetica.
[Publications] R.Okazaki: "On Parities of Relative Class Numbers of Certain CM-Extensions"ASPM of Math. Soc. Japan. 30. 419-444 (2001)
[Publications] H.Terao: "Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss-Manin connections"Topology and Its Appl.. 118. 255-274 (2002)
[Publications] H.Terao: "Algebras generated by reciprocals of linear forms"J.of Algebra.
[Publications] K.Miyake: "Some Aspects on Interactions between Algebraic Number Theory and Analytic Number Theory"Number Theoretic Methods-Future Trends.

2001 Fiscal Year Annual Research Report

数論アルゴリズムの研究と数論システムの開発

Principal Investigator

中村 憲 東京都立大学, 理学研究科, 教授 (80110849)

Research Products

[Publications] H.M.Bahig, H.El-Zahar, K.Nakamura: "Some results for some conjectures in addition chains"Combinatrics, Computability and Logic (DMTCS'01). 47-54 (2001)

[Publications] H.M.Bahig, K.Nakamula: "Some properties of nonstar steps in addition chains and new cases where the Scholz conjecture is true"J.Algorithms. (2002)

[Publications] T.Kurata: "Intersection and singleton type assignment characterizing finite Bohm-trees"Information and Computation.

[Publications] H.Ishihara, T.Kurata: "Completeness of intersection and union type assignment systems for call-by-value λ-models"Theoretical Computer Science. 272. 197-221 (2002)

[Publications] M.Kida: "Nonexistence of elliptic curves having good reduction everywhere over certain quadratic fields"Arch.Math.(Basel). 76. 436-440 (2001)

[Publications] M.Kida: "Good reduction of elliptic curves over imaginary quadratic fields"Journal de Theorie de Nombres de Bordeaux. 13. 201-209 (2001)

[Publications] M.Kida: "Computing elliptic curves having good reduction everywhere over quadratic fields"Tokyo J.Math.. 24. 545-558 (2001)

[Publications] T.Izu, J.Kogure, M.Noro, K.Yokoyama: "Order counting of elliptic curves defined over finite fields of characteristic 2"Electorinics and Communications in Japan Part III, -Fundamental Electoric Science. 85・1. 62-70 (2002)

[Publications] M.Noro, K.Yokoyama: "Yet another practical implementation of polynomial factorization over finite finite fields"ISSAC 2002.

[Publications] K.Yamamura: "Maximal unramified extensions of imaginary quadratic number fields of small conductors II"Journal de Theorie des Nombres de Bordeaux. 13・2. (2001)

[Publications] T.Fukuda, K.Komatsu: "On Iwasawa λ_3-invariants of cyclic cubic fields of prime conductor"Math.Comp.. 70・236. 1707-1712 (2001)

[Publications] T.Fukuda, K.Komatsu: "An application of Siegel modular functions to Kronecker's limit formula"LNCS. (2002)

[Publications] H.Srivastava, H.Tsumura: "Certain classes of rapidly convergent series representations for L(2n, x) and L(2n+1, x)"Acta Arithmetica. 100. 195-201 (2001)

[Publications] K.Kozuka, H.Tsumura: "On some modules attached to the Lubin-Tate formal groups"Tokyo J.Math.. 23. 442-465 (2001)

[Publications] H.Tsumura: "On modification of the q-L-series and its applications"Nagoya Math.J.. 164. 185-197 (2001)

[Publications] H.Tsumura: "On some combinatorial relations for Tohnheim's double series"Acta Arithmetica.

[Publications] R.Okazaki: "On Parities of Relative Class Numbers of Certain CM-Extensions"ASPM of Math. Soc. Japan. 30. 419-444 (2001)

[Publications] H.Terao: "Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss-Manin connections"Topology and Its Appl.. 118. 255-274 (2002)

[Publications] H.Terao: "Algebras generated by reciprocals of linear forms"J.of Algebra.

[Publications] K.Miyake: "Some Aspects on Interactions between Algebraic Number Theory and Analytic Number Theory"Number Theoretic Methods-Future Trends.

中村憲東京都立大学, 理学研究科, 教授 (80110849)