Solvability of systems of diagonal equations over p-adic local fields

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that a system of (Formula presented.) diagonal equations of degree (Formula presented.) over a finite extension (Formula presented.) of (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.) (if (Formula presented.)) or (Formula presented.) (if (Formula presented.)). As a consequence, a system of (Formula presented.) homogeneous equations of degree (Formula presented.) over (Formula presented.) has a non-trivial solution in (Formula presented.) if the number of variables exceeds (Formula presented.).

Original languageEnglish (US)
Pages (from-to)207-228
Number of pages22
JournalProceedings of the London Mathematical Society
Volume122
Issue number2
DOIs
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 11D72
  • 11D88 (primary)
  • 11E76
  • 11G25 (secondary)

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