Number-theoretic properties of certain CR mappings

John P. D'Angelo

Research output: Contribution to journalArticlepeer-review


We first prove a uniqueness result for certain group-invariant CR mappings to hyperquadrics. For cyclic groups these mappings lead to a collection of polynomials f p,q (with integer coefficients) in two variables; here p and q are positive integers. We use the uniqueness result to prove some surprising number-theoretic results about the f p,q, in particular, f p,q is congruent to x P+y P modulo (p) (for P ≥ 2) if and only if p is prime. We also determine recurrence relations for these polynomials for q ≤ 3 and determine a functional equation for a generating function. Finally, we discuss the invariant polynomials that arise for certain representations of dihedral groups to illustrate the non-Abelian case.

Original languageEnglish (US)
Pages (from-to)215-229
Number of pages15
JournalJournal of Geometric Analysis
Issue number2
StatePublished - 2004


  • CR mappings
  • Lens spaces
  • congruences
  • finite unitary groups
  • hyperquadrics
  • invariant polynomials
  • primality
  • recurrence relations

ASJC Scopus subject areas

  • Geometry and Topology


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