APPLICATIONS OF CLASS NUMBERS AND BERNOULLI NUMBERS TO HARMONIC TYPE SUMS

Goral H., Sertbas D. C.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.58, no.6, pp.1463-1481, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.4134/bkms.b201045
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1463-1481
  • Keywords: &nbsp, Harmonic numbers, Bernoulli numbers, regular primes, class number, IRREGULAR PRIMES, CYCLOTOMIC INVARIANTS
  • Çukurova University Affiliated: No

Abstract

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.