Buffons Nadelproblem und verwandte probleme behandelt mit der Theorie der Gleichverteilung: Teil II

✍ Scribed by Edmund Hlawka

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 233 KB
• Volume: 44
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147746

✦ Synopsis

ABSTgACT. We denote with PC" the m-dimensional complex projective space, with U the unitary group acting on it with zi(j = O, 1 ..... m) the homogenous coordinates of a point [z] of PC" and assume that the zl are normalized such that z0~ 0 + ... -I-z,,~m = 1. Furthermore we denote the U-invariant metric on PC" with d. We consider now a uniformly distributed sequence ([Z]k; k = 1,2,...) of points on PC" and study the sequence (dl([Z]k, [z]0)), l ~> 0, [Z]0 a fixed point. We prove with the help of the theory of uniform distribution properties of this sequence. We consider furthermore a dual sequence suggested by the theory of H. Weyl and L.V. Ahlfors on meromorphic curves.