A short note on some arithmetical properties of the integer part of αp

Akbal Y.

Turkish Journal of Mathematics, cilt.43, sa.3, ss.1253-1262, 2019 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1809-43
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1253-1262
  • Anahtar Kelimeler: Arithmetic progressions, Beatty sequences, Exponential sums, Shifted primes
  • TED Üniversitesi Adresli: Hayır

Özet

Let α > 0 be an irrational number. We study some of the arithmetical properties of [⌊αp⌋]p=2∞, where p denotes a prime number and ⌊x⌋ denotes the largest integer not exceeding x.