Applications of Class Numbers and Bernoulli Numbers to Harmonic Type Sums
Bull. Korean Math. Soc.
Published online July 7, 2021
Haydar Goral and Doga Can Sertbas
Izmir Institute of Technology; Cukurova University
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.
Keywords : harmonic numbers, Bernoulli numbers, regular primes, class number
MSC numbers : 11B83, 11B68, 5A10
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd