1991 Fiscal Year Annual Research Report

関数方程式と超越数論

Research Project

Project/Area Number	03640092
Research Institution	Keio University
Principal Investigator	塩川宇賢慶應義塾大学, 理工学部・数理科学科, 教授 (00015835)
Co-Investigator(Kenkyū-buntansha)	仲田均慶應義塾大学, 理工学部・数理科学科, 助教授 (40118980) 渋谷政昭慶應義塾大学, 理工学部・数理科学科, 教授 (20146723) 榎本彦衛慶應義塾大学, 理工学部・数理科学科, 教授 (00011669) 菊地紀夫慶應義塾大学, 理工学部・数理科学科, 教授 (80090041) 伊藤雄二慶應義塾大学, 理工学部・数理科学科, 教授 (90112987)
Keywords	代数的独立性 / 超越数とMahlerの方法 / 数列のcomplexity / ビリヤ-ドに関するRauzy予想 / 正規数の構成 / ラプラシアンの行列式 / セルバ-グ.ゼ-タ / パンルヴェ方程式
Research Abstract	本研究の主な成果を列記する。研究の背景,相互の関連及び証明については、申請書及び別紙論文リストを参照されたい。1)関数f(z)=Σ__<n≧1>[θn+φ]z^nの代数点での値の代数的独立性が証明された。これはある2変数関数の関数方程式から得られる。2) 1)の応用として,2次元ビリヤ-ドにより定義される数列{[θn+φ]}n≧1の具体的記述が与えられる。3).3次元ビリヤ-ドにより定義される数列の複雑さに関するRauzy予想を証明した。又この数列の具体的記述も出来た。4)0以外の元が正規数であるような実数の部分環を具体的な構成することに成功した。5)多項式により生成される正規数及び素数列により生成される正規数に対して最良のdiscrepanuy評価を与えた。(以上塩川)。6)ある種の代数方程式のガロア群がSn(対称群)であることが示された(小松)。7)いくつかのセルバ-ク・ゼ-タ関数がラプラシアやルエル作用素の行列式で表示できることを示した。(小山)。8)ある拡大がパンルヴェ・梅村拡大に含まれるならば,それ自身パンルヴェ・梅村拡大であることが証明された(西岡)。9)パンルヴェ(V)などの非線形方程式の解の漸近的挙動を表わす表示式を得た(下村)。10)変分問題のモ-ス流の掲成法を提案し,その近似解の評価を求め,いくつかの変分問題においてモ-ス流の存在を示した。(菊地)。11)グラフに因子が存在するための(グラフの項点数と無関数な)十分条件を与えた。又3連結グラフの可縮辺についての研究を行った。(大田)。12) 完全2部グラフの星型樹化数の上限と下限を与え,それらが結列な場合に一致することを示した。また{1,3,…,2nー1}を和がkの部分集合の分割できるための必要十分条件をkが偶数の場合に解決した(榎本)。13)、ガウス数体上の連分数のmetrical theoryのアイディアをHeche群の連分数に適用して種々な結果を得た。

Research Products

(37 results)

All Other

All Publications (37 results)

[Publications] Y.Nakai and I.Shiokawa: "Discrepancy estimates of a class of nornaal numbers." Acta Arithmetica.
[Publications] H.kano and I.Shiokawa: "Rings of normal and nonnormal numbers." プレプリント Research Report KSTS/RRー91/006. 1-17 (1991)
[Publications] P.Arnoux,Ch.Mauduit,I.Shiokawa and J.Tamura: "Complexity of sequences defined by silliard in the cube." プレプリント.Prepublications Math.de l'uniuersite Paris VII. N°17. 1-10 (1992)
[Publications] I.Shiokawa and J.Tamura: "Description of sequences defined by hilliard in the cube." プレプリント.(1992)
[Publications] I.Shiokawa: "On the normal number defined by primes" プレプリント. (1992)
[Publications] I.Shiokawa,J.Tamura.他.: "A conjecture of Rauzy on complexity of certain sequcnces." プレプリント. (1992)
[Publications] H.Enomoto and Y.Usami: "The star arboucity of complete bipartite graphs" Yraph Theory,Combinatorics,and Applications.(John Wiley & Sons.Inc.). 389-396 (1991)
[Publications] H.Enomoto,M.Mizutani,N.Tokushige: "A word pwbem in Coxeter semigroups." Discute Math.
[Publications] H.Enomoto and M.Kano.: "Disjoint odd integer subsets having a constant even sum."
[Publications] H.Nakada: "The nutrical theory of wntinued fractrons" Acts Arithmetica. 56. 279-289 (1991)
[Publications] N.Kikuchi.: "An approach to the construction of Morse flows for variational functionals." NematicsーMathematical and Physical Aspects ed:J.M.Coron et al,Nato Adv.Sci.Inst.Ser C:Math.Phys.Sci.332. (1991)
[Publications] N.Kikuchi: "Holder estimates of solutions for differenceーdefferential equations of ellipticーParabolic type" Numerische Mathematik.
[Publications] K.Nishioka,I.Shiwkawa and J.Tamura.: "Auihmetical pwperties of certoin power series." J.Number Theory.
[Publications] N.Kikuchi: "Kneser's property for a parabolic partial differential equation" J.of Nonlinear Analysis:Theory,Methods,and Applecations.
[Publications] S.Koyama.: "Determinant expression of Selberg zeta functions(I)" Trans.A.M.S.324. 149-168 (1991)
[Publications] S.Koyama: "Determinant expression of Selberg zeta function(II)" TranS.A.M.S.
[Publications] S.Koyama: "Determinant expression of selberg zeta function(III)" Proc.A.M.S.113. 303-312 (1991)
[Publications] S.Koyama: "Zeta Functions of loop groups." Adv.Stud.Pure Math.21. 227-235 (1992)
[Publications] S.Koyama: "Selberg zeta functions and Ruelle operators for function fields" Proc.Japan Acad.67A. 255-259 (1991)
[Publications] S.Koyama: "Selberg zeta functions for PSL and PGL." プレプリント.
[Publications] Y.Egawa and K.Ota: "Regular factors in K_<1,n>ーfru graphs." J.of greph Minon Theory.15. 337-344 (1991)
[Publications] N.Dean and K.Ota: "2ーfactors,connectivity and graph minors" Proc.of graph conference.
[Publications] R.E.L.Aldred,R.L.Hemminger,and K.Ota: "The 3ーconnected graphs having a longest cycle contarning only three contrbctible edges."
[Publications] W.McCuaig and K.Ota: "Contractible triples in 3ーconnected graphs"
[Publications] K.Nishioka: "PainleveーUmemura extensions." プレプリント.
[Publications] K.Komatsu: "Squareーfree discriminants and affectーfree equations." Tokyo J.Math.14. 57-60 (1991)
[Publications] K.komatsu: "On the Galois group of x^p+ax+a=0." Tokyo.J.Math.14. 227-229 (1991)
[Publications] K.Komatsu: "On the Galvis group of x^n-x^<n-1>-x^<n-2>-…-x-1=0" Keiv Science and Technology Reports. 44. 1-6 (1991)
[Publications] K.Komatsu: "On certain affectーfree equatrons"
[Publications] K.Komatsu: "On the Galois group of x^p+p^t b(x+1)=0."
[Publications] H.Tsubaki: "A test for dose dependency of drug efficacy through dose escalation design." Bull.Biometric Soc.of Japan. 12. 73-84 (1991)
[Publications] S.Shimomura: "On an asymptotic property of a nonlinear ordinary differential equation" Tokyo J.Math.14. 329-340 (1991)
[Publications] M.Shibuya: "A simplified proof of a Bonferroniーtype inequality by Tan and Xu and its extension." Stat.and Prob.Letters. 11. 255-257 (1991)
[Publications] M.Shibuya: "An idevtity for sums of binomial coefficients" SIAM Review 33,116.(Problem 91ー5). 33. (1991)
[Publications] M.Shibuya: "Bonferroniーtype inequalities:Chebyshevーtype inequalities for the probahility distributions on[0,n]" Ann.Inst.Statist.Math.43. 261-285 (1991)
[Publications] M.Shibuya and R.Shibata: "User interface provided by Data and Descieption" Bull.of the international Statistical Institute. (1991)
[Publications] M.Shibuya: "Sharp Bonferroniーtype inequalitios in explicit forms" Probability thevry and Applications,J.Mogyorodi Memorial volume.(1992)

1991 Fiscal Year Annual Research Report

関数方程式と超越数論

Principal Investigator

塩川 宇賢 慶應義塾大学, 理工学部・数理科学科, 教授 (00015835)

Research Products

[Publications] Y.Nakai and I.Shiokawa: "Discrepancy estimates of a class of nornaal numbers." Acta Arithmetica.

[Publications] H.kano and I.Shiokawa: "Rings of normal and nonnormal numbers." プレプリント Research Report KSTS/RRー91/006. 1-17 (1991)

[Publications] P.Arnoux,Ch.Mauduit,I.Shiokawa and J.Tamura: "Complexity of sequences defined by silliard in the cube." プレプリント.Prepublications Math.de l'uniuersite Paris VII. N°17. 1-10 (1992)

[Publications] I.Shiokawa and J.Tamura: "Description of sequences defined by hilliard in the cube." プレプリント.(1992)

[Publications] I.Shiokawa: "On the normal number defined by primes" プレプリント. (1992)

[Publications] I.Shiokawa,J.Tamura.他.: "A conjecture of Rauzy on complexity of certain sequcnces." プレプリント. (1992)

[Publications] H.Enomoto and Y.Usami: "The star arboucity of complete bipartite graphs" Yraph Theory,Combinatorics,and Applications.(John Wiley & Sons.Inc.). 389-396 (1991)

[Publications] H.Enomoto,M.Mizutani,N.Tokushige: "A word pwbem in Coxeter semigroups." Discute Math.

[Publications] H.Enomoto and M.Kano.: "Disjoint odd integer subsets having a constant even sum."

[Publications] H.Nakada: "The nutrical theory of wntinued fractrons" Acts Arithmetica. 56. 279-289 (1991)

[Publications] N.Kikuchi.: "An approach to the construction of Morse flows for variational functionals." NematicsーMathematical and Physical Aspects ed:J.M.Coron et al,Nato Adv.Sci.Inst.Ser C:Math.Phys.Sci.332. (1991)

[Publications] N.Kikuchi: "Holder estimates of solutions for differenceーdefferential equations of ellipticーParabolic type" Numerische Mathematik.

[Publications] K.Nishioka,I.Shiwkawa and J.Tamura.: "Auihmetical pwperties of certoin power series." J.Number Theory.

[Publications] N.Kikuchi: "Kneser's property for a parabolic partial differential equation" J.of Nonlinear Analysis:Theory,Methods,and Applecations.

[Publications] S.Koyama.: "Determinant expression of Selberg zeta functions(I)" Trans.A.M.S.324. 149-168 (1991)

[Publications] S.Koyama: "Determinant expression of Selberg zeta function(II)" TranS.A.M.S.

[Publications] S.Koyama: "Determinant expression of selberg zeta function(III)" Proc.A.M.S.113. 303-312 (1991)

[Publications] S.Koyama: "Zeta Functions of loop groups." Adv.Stud.Pure Math.21. 227-235 (1992)

[Publications] S.Koyama: "Selberg zeta functions and Ruelle operators for function fields" Proc.Japan Acad.67A. 255-259 (1991)

[Publications] S.Koyama: "Selberg zeta functions for PSL and PGL." プレプリント.

[Publications] Y.Egawa and K.Ota: "Regular factors in K_<1,n>ーfru graphs." J.of greph Minon Theory.15. 337-344 (1991)

[Publications] N.Dean and K.Ota: "2ーfactors,connectivity and graph minors" Proc.of graph conference.

[Publications] R.E.L.Aldred,R.L.Hemminger,and K.Ota: "The 3ーconnected graphs having a longest cycle contarning only three contrbctible edges."

[Publications] W.McCuaig and K.Ota: "Contractible triples in 3ーconnected graphs"

[Publications] K.Nishioka: "PainleveーUmemura extensions." プレプリント.

[Publications] K.Komatsu: "Squareーfree discriminants and affectーfree equations." Tokyo J.Math.14. 57-60 (1991)

[Publications] K.komatsu: "On the Galois group of x^p+ax+a=0." Tokyo.J.Math.14. 227-229 (1991)

[Publications] K.Komatsu: "On the Galvis group of x^n-x^<n-1>-x^<n-2>-…-x-1=0" Keiv Science and Technology Reports. 44. 1-6 (1991)

[Publications] K.Komatsu: "On certain affectーfree equatrons"

[Publications] K.Komatsu: "On the Galois group of x^p+p^t b(x+1)=0."

[Publications] H.Tsubaki: "A test for dose dependency of drug efficacy through dose escalation design." Bull.Biometric Soc.of Japan. 12. 73-84 (1991)

[Publications] S.Shimomura: "On an asymptotic property of a nonlinear ordinary differential equation" Tokyo J.Math.14. 329-340 (1991)

[Publications] M.Shibuya: "A simplified proof of a Bonferroniーtype inequality by Tan and Xu and its extension." Stat.and Prob.Letters. 11. 255-257 (1991)

[Publications] M.Shibuya: "An idevtity for sums of binomial coefficients" SIAM Review 33,116.(Problem 91ー5). 33. (1991)

[Publications] M.Shibuya: "Bonferroniーtype inequalities:Chebyshevーtype inequalities for the probahility distributions on[0,n]" Ann.Inst.Statist.Math.43. 261-285 (1991)

[Publications] M.Shibuya and R.Shibata: "User interface provided by Data and Descieption" Bull.of the international Statistical Institute. (1991)

[Publications] M.Shibuya: "Sharp Bonferroniーtype inequalitios in explicit forms" Probability thevry and Applications,J.Mogyorodi Memorial volume.(1992)

塩川宇賢慶應義塾大学, 理工学部・数理科学科, 教授 (00015835)