Kodai Mathematical Journal

On the multiple values of algebroid functions

Zongsheng Gao

2000 Volume 23 Issue 2 Pages 151-163
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044207

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For any v-valued algebroid function of finite order ρ>0 in |z|<∞, we prove the existence of the sequence of filling disks and Borel direction dealing with its multiple values.

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On value distribution of entire maps of C² to C²

Yukinobu Adachi

2000 Volume 23 Issue 2 Pages 164-170
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044208

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Geometric probabilities concerning large random triangles in the hyperbolic plane

Yukinao Isokawa

2000 Volume 23 Issue 2 Pages 171-186
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044209

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Concerning a random triangle on a disk D_R of radius R in the hyperbolic plane, the following four geometric probabilities are studied: (i) the probability p_a(R) that a random triangle is acute; (ii) the probability p_o(R) that a random triangle has the orthocenter; (iii) the probability p_e(R) that a random triangle has at least one of the three excenters; and (iv) the probability p_c(R) that a random triangle has the circumcenter. It is shown that, as R tends to the infinity, both the probability p_a(R) and p_o(R) tend to one, whereas the probability p_e(R) tends to zero. Moreover it is shown that the probability p_c(R) tends to a limit p_c, which can be expressed as a certain expectation concerning a random triangle in the Euclidean plane. To evaluate this expectation numerically, we obtain 0.45962039 as an estimate for p_c.

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Involutions fixing the disjoint union of 3-real projective space with Dold manifold

Zhi Lü, Xibo Liu

2000 Volume 23 Issue 2 Pages 187-213
Published: 2000
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2996/kmj/1138044210

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In this paper, we determine the existence of all involutions fixing a disjoint union of 3-real projective space RP(3) with Dold manifold under the condition that the normal bundle to RP(3) does not bound, and also study the representatives up to bordism of those involutions which exist.

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Lines on Brieskorn-Pham surfaces

Guangfeng Jiang, Mutsuo Oka, Tai Pho Duc, Dirk Siersma

2000 Volume 23 Issue 2 Pages 214-223
Published: 2000
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2996/kmj/1138044211

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By using toric modifications and a result of Gonzalez-Sprinberg and Lejeune-Jalabert, we answer the following questions completely. On which Brieskorn-Pham surface there exist smooth curves passing through the singular point? If there exist, how “many” and what are the defining equations?

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Hyperbolic hypersurfaces in the complex projective spaces of low dimensions

Manabu Shirosaki

2000 Volume 23 Issue 2 Pages 224-233
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044212

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On recurrence for self-similar additive processes

Kouji Yamamuro

2000 Volume 23 Issue 2 Pages 234-241
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044213

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Picard constants of three-sheeted algebroid surfaces with p(y)=5

Kazunari Sawada

2000 Volume 23 Issue 2 Pages 242-254
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044214

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In 1995 Sawada-Tohge proved that every three-sheeted algebroid Riemann surface with p(y)=5 is of Picard constant 5, unless its discriminant has a form e^δH(Ae^4H+B), where δ=0 or 1. In this paper we shall prove that the result remains valid with no condition.

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On special values of standard L-functions attached to vector valued Siegel modular forms

Noritomo Kozima

2000 Volume 23 Issue 2 Pages 255-265
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044215

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Symmetric weights and s-representations

Sergio Console, Anna Fino

2000 Volume 23 Issue 2 Pages 266-280
Published: 2000
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2996/kmj/1138044216

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We study irreducible representations of compact Lie groups relating an algebraic condition (the highest weight λ is “symmetric”, i.e., in any simple factor all non zero <λ, α> are equal, for any positive root α and any invariant inner product) with a geometric one (for all orbits, the d-th osculating space coincides with the representation space).
We prove that, if d=2 and λ is symmetric, the irreducible representation with highest weight λ corresponds to the isotropy representation of a symmetric space.

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A note on necessary conditions of hypoellipticity for some classes of differential operators with double characteristics

Nguyen Minh Tri

2000 Volume 23 Issue 2 Pages 281-296
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044217

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We construct explicit formulas for fundamental solutions and global non-smooth solutions at degenerate points of some classes of differential operators with double characteristics. A new elementary proof for non-hypoellipticity is given.

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On a duality theorem of abelian varieties over higher dimensional local fields

Yoshihiro Koya

2000 Volume 23 Issue 2 Pages 297-308
Published: 2000
Released on J-STAGE: January 21, 2009

DOIhttps://doi.org/10.2996/kmj/1138044218

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In this paper, we prove a duality theorem of abelian varieties over higher dimensional local fields under some conditions. It might be a one of generalization of the classical Tate duality theorem of abelian varieties over local fields.

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