Value sets of Lattes maps over finite fields

Kucuksakalli O.

JOURNAL OF NUMBER THEORY, cilt.143, ss.262-278, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 143
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.jnt.2014.04.014
  • Dergi Adı: JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.262-278
  • Anahtar Kelimeler: Dickson polynomial, Lattes map, Elliptic curve, Complex multiplication, Permutation
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication. (C) 2014 Elsevier Inc. All rights reserved.