On the symmetric determinantal representations of the Fermat curves of prime degree

Yasuhiro Ishitsuka, Tetsushi Ito

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross-Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.

Original languageEnglish
Pages (from-to)955-967
Number of pages13
JournalInternational Journal of Number Theory
Volume12
Issue number4
DOIs
Publication statusPublished - Jun 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On the symmetric determinantal representations of the Fermat curves of prime degree'. Together they form a unique fingerprint.

Cite this