APPLICATIONS OF CLASS NUMBERS AND BERNOULLI NUMBERS TO HARMONIC TYPE SUMS

Goral, Haydar; Sertbas, DOĞA

doi:10.4134/bkms.b201045

APPLICATIONS OF CLASS NUMBERS AND BERNOULLI NUMBERS TO HARMONIC TYPE SUMS

Goral H., Sertbas D. C.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.58, sa.6, ss.1463-1481, 2021 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 58 Sayı: 6
Basım Tarihi: 2021
Doi Numarası: 10.4134/bkms.b201045
Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Sayfa Sayıları: ss.1463-1481
Anahtar Kelimeler: &nbsp, Harmonic numbers, Bernoulli numbers, regular primes, class number, IRREGULAR PRIMES, CYCLOTOMIC INVARIANTS
Çukurova Üniversitesi Adresli: Hayır

Özet

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.