1989 Fiscal Year Annual Research Report

整数論

Research Project

Project/Area Number	63540060
Research Institution	Saga University
Principal Investigator	中原徹佐賀大学, 理工学部, 教授 (50039278)
Co-Investigator(Kenkyū-buntansha)	三苫至佐賀大学, 理工学部, 助教授 (40112289) 西晃央佐賀大学, 教育学部, 助教授 (60022274) 上野一男佐賀大学, 教養学部, 助教授 (10193822) 田中達治佐賀大学, 教養学部, 助教授 (80039370) 上原健佐賀大学, 理工学部, 教授 (80093970)
Keywords	2次体 / 類数の可除性 / 単数 / 整数環の巾底 / 類数公式 / 局所体 / chow形式 / 量子空間
Research Abstract	1.(1)Scholz-Redei-Reichardtの鏡像定理に関連して提起されたT.P.Vaughanの問題[Acta Arith.1984年]は当代表者により肯定的に解決された。2次体の類数の可除性と単数についての仕事[T.Nakahara,Rep.Fac.Sci.Engrg.Saga Univ.Math.,1978年]の一応用として初等的な証明を与えた[Proceedings in Budapest Number Theory Conference,to appear.](2)S.KitamuraとY.Oshimaとの共同研究であるグラフ理論を援用した2次体の類群の4-階数評価はT.Uehara[J.Number Theory,Vol.31,1989年]の異なる方向からの研究を促した。(3)5と異なる素数導手の4次巡回体Kの整数環はZ-自由加群として巾底をもたないことをKの2次部分体の情報のみで制御する方法を考案して、大学院生K.Kogaとの共同研究で示した。この計算手法は既知の結果[T.Nakahara,Monatshefte fuer Math.,Vol.94,1982年]よりも簡明である。 2.2次体の狭義イデアル類群の4階数について、実2次体とそれに対応する虚2次体との4階数が等しくなるための必要十分条件を不定方程式を使って記述できた。ディリクレの類数公式を2進体上の局所体で級数展開するという手法で、複数個の2次体の類数と単数に関する、2の高い巾を法とした、一般的合同関係式を得た。 3.射影空間に埋め込まれた代数多様体上の有限個の点がchow形式を定める為の条件について、generic projectionの定義方程式を求めるという立場から考察している。一般のlinear projectionの下でのchow形式の挙動を解明した。現在この立場から現れるある種の不変式の性質を調べている。 4.超対称的場の量子論におけるラプラシアンが作用する無限次元のホウムの空間間を設定しDeRham-Hodge-Kodairaの分解定理を得た。

Research Products
(19 results)

All Other

All Publications (19 results)

[Publications] T.Nakahara: "A construction of quadratic fields whose class numbers are divisible by a power of 3" Proceedings of Budapest Number Theory conference.
[Publications] T.Uehara: "On the 4-rank of the narrow ideal class group of a quadratic field" J.Number Theory. 31. 167-173 (1989)
[Publications] T.Uehara: "On linear congruence relations between class numbers of quadratic fields" J.Number Theory.
[Publications] T.Tanaka: "On the Behaviours of Chow-Forms Under a Linear Projection" Rep.Fac.Sci.Engrg.Saga Univ.Math.18. 1-4 (1990)
[Publications] K.Ueno: "General power umbral calculus in several variables" J.Pure Appl.Algebra. 59. 299-308 (1989)
[Publications] K.Ueno: "Hypergeometric series formulas through operator calculus" Funkcial.Ekvac.
[Publications] K.Ueno: "Hypergeometric series formulas generated by the chu-Vandermonde convolution" Mem.Faculty of Science,Ser.A,Kyushu Univ.
[Publications] A.Nishi: "A proof of the Jensen's“strict"inequality" Int.J.math.Educ.Sci Technol.
[Publications] A.NIshi: "Inductive proof on the implicit function theorem" i.b.i.d.
[Publications] Y.Ogura: "One-dimensional bi-generalized diffusion processes" J.Math.Soc.Japan. 41. 213-242 (1989)
[Publications] N.Ikeda and Y.Ogura: "A degenarating sequence of Riemannian metrics on a manifold and their Brownian motions" Proceedings of the Conference on Diffusion Processes and Related Problems in Analysis.
[Publications] G.Kallianpur,I.Mitoma and R.L.Wolpert: "Diffusion equations in duals of nuclear spaces" Stochastics.
[Publications] M.Kazaki and H.Sumi: "On normal forms of Laplacian and its iterations in harmonic spaces" Comm.Math.Univ.Carolinae.
[Publications] M.Kozaki: "On mean value theorems for small geodesic spheres in Riemannian manifolds" Preprint.
[Publications] Y.Furusho: "Existence of global positive solutions of quasilinear elliptic equations in unbounded domains" Funkcial.Ekvac.82. 227-242 (1989)
[Publications] Y.Ebihara and Y.Furusho: "On the exterior Dirichlet problem for semilinear elliptic equations with coefficients unbounded on the boundary" Hiroshima Math.J.19. 379-396 (1989)
[Publications] Y.Furusho: "Existence of positive entire solutions for a class of quasilinear elliptic equations" J.Math.Anal.Appl.
[Publications] Y.Ebihara and Y.Furusho: "On some semilinear parabolic equations with unbounded coefficients in exterior domain" Funkcial.Ekvac.,14 pages.
[Publications] Y.Senba,Y.Ebihara and Y.Furusho: "Dirichlet problem for a semilinear elliptic equation with singular coefficien" Nonlinear Anal.,17 pages.

1989 Fiscal Year Annual Research Report

整数論

Principal Investigator

中原 徹 佐賀大学, 理工学部, 教授 (50039278)

Research Products

[Publications] T.Nakahara: "A construction of quadratic fields whose class numbers are divisible by a power of 3" Proceedings of Budapest Number Theory conference.

[Publications] T.Uehara: "On the 4-rank of the narrow ideal class group of a quadratic field" J.Number Theory. 31. 167-173 (1989)

[Publications] T.Uehara: "On linear congruence relations between class numbers of quadratic fields" J.Number Theory.

[Publications] T.Tanaka: "On the Behaviours of Chow-Forms Under a Linear Projection" Rep.Fac.Sci.Engrg.Saga Univ.Math.18. 1-4 (1990)

[Publications] K.Ueno: "General power umbral calculus in several variables" J.Pure Appl.Algebra. 59. 299-308 (1989)

[Publications] K.Ueno: "Hypergeometric series formulas through operator calculus" Funkcial.Ekvac.

[Publications] K.Ueno: "Hypergeometric series formulas generated by the chu-Vandermonde convolution" Mem.Faculty of Science,Ser.A,Kyushu Univ.

[Publications] A.Nishi: "A proof of the Jensen's“strict"inequality" Int.J.math.Educ.Sci Technol.

[Publications] A.NIshi: "Inductive proof on the implicit function theorem" i.b.i.d.

[Publications] Y.Ogura: "One-dimensional bi-generalized diffusion processes" J.Math.Soc.Japan. 41. 213-242 (1989)

[Publications] N.Ikeda and Y.Ogura: "A degenarating sequence of Riemannian metrics on a manifold and their Brownian motions" Proceedings of the Conference on Diffusion Processes and Related Problems in Analysis.

[Publications] G.Kallianpur,I.Mitoma and R.L.Wolpert: "Diffusion equations in duals of nuclear spaces" Stochastics.

[Publications] M.Kazaki and H.Sumi: "On normal forms of Laplacian and its iterations in harmonic spaces" Comm.Math.Univ.Carolinae.

[Publications] M.Kozaki: "On mean value theorems for small geodesic spheres in Riemannian manifolds" Preprint.

[Publications] Y.Furusho: "Existence of global positive solutions of quasilinear elliptic equations in unbounded domains" Funkcial.Ekvac.82. 227-242 (1989)

[Publications] Y.Ebihara and Y.Furusho: "On the exterior Dirichlet problem for semilinear elliptic equations with coefficients unbounded on the boundary" Hiroshima Math.J.19. 379-396 (1989)

[Publications] Y.Furusho: "Existence of positive entire solutions for a class of quasilinear elliptic equations" J.Math.Anal.Appl.

[Publications] Y.Ebihara and Y.Furusho: "On some semilinear parabolic equations with unbounded coefficients in exterior domain" Funkcial.Ekvac.,14 pages.

[Publications] Y.Senba,Y.Ebihara and Y.Furusho: "Dirichlet problem for a semilinear elliptic equation with singular coefficien" Nonlinear Anal.,17 pages.

中原徹佐賀大学, 理工学部, 教授 (50039278)