Criteria for periodicity and an application to elliptic functions

Research output: Contribution to journalArticlepeer-review

Abstract

Let P and Q be relatively prime integers greater than 1, and let f be a real valued discretely supported function on a finite dimensional real vector space V. We prove that if fP(x) = f (Px) - f (x) and fQ(x) = f (Qx) - f (x) are both Λ-periodic for some lattice Λ ⊂ V, then so is f (up to a modification at ý). This result is used to prove a theorem on the arithmetic of elliptic function fields. In the last section, we discuss the higher rank analogue of this theoremand explain why it fails in rank 2. A full discussion of the higher rank case will appear in a forthcoming work.

Original languageAmerican English
Pages (from-to)530-540
Number of pages11
JournalCanadian Mathematical Bulletin
Volume64
Issue number3
DOIs
StatePublished - 14 Aug 2020

Keywords

  • Difference equations
  • Elliptic functions
  • Periodic functions

All Science Journal Classification (ASJC) codes

  • General Mathematics

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