Upper bounds on cyclotomic numbers

Koichi Betsumiya, Mitsugu Hirasaka, Takao Komatsu, Akihiro Munemasa

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we give upper bounds for cyclotomic numbers of order e over a finite field with q elements, where e is a positive divisor of q - 1. In particular, we show that under certain assumptions, cyclotomic numbers are at most ⌈k2⌉, and the cyclotomic number (0, 0) is at most ⌈k2⌉-1, where k=(q-1)/e. These results are obtained by using a known formula for the determinant of a matrix whose entries are binomial coefficients.

Original languageEnglish
Pages (from-to)111-120
Number of pages10
JournalLinear Algebra and Its Applications
Volume438
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Keywords

  • Cyclotomic numbers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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