An explicit formula for the discrete power function associated with circle patterns of schramm type

Hisashi Ando, Mike Hay, Kenji Kajiwara, Tetsu Masuda

研究成果: Contribution to journalArticle査読

6 被引用数 (Scopus)

抄録

We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric τ functions for the sixth Painlevé equation. The original definition of the discrete power function imposes strict conditions on the domain and the value of the exponent. However, we show that one can extend the value of the exponent to arbitrary complex numbers except even integers and the domain to a discrete analogue of the Riemann surface. Moreover, we show that the discrete power function is an immersion when the real part of the exponent is equal to one.

本文言語英語
ページ(範囲)1-41
ページ数41
ジャーナルFunkcialaj Ekvacioj
57
1
DOI
出版ステータス出版済み - 2014

All Science Journal Classification (ASJC) codes

  • 分析
  • 代数と数論
  • 幾何学とトポロジー

フィンガープリント

「An explicit formula for the discrete power function associated with circle patterns of schramm type」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル