THE DIFFERENCE OF HYPERHARMONIC NUMBERS VIA GEOMETRIC AND ANALYTIC METHODS

Altuntaş Ç., Goral H., SERTBAŞ D. C.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.59, sa.6, ss.1103-1137, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.4134/jkms.j210630
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1103-1137
  • Anahtar Kelimeler: Harmonic numbers, arithmetic geometry, prime numbers
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finite-ness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyper -harmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.