## Abstract

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 language | English (US) |
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Pages (from-to) | 215-229 |

Number of pages | 15 |

Journal | Journal of Geometric Analysis |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - 2004 |

## Keywords

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

## ASJC Scopus subject areas

- Geometry and Topology