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Citation - WoS: 2
Citation - Scopus: 1
The Difference of Hyperharmonic Numbers Via Geometric and Analytic Methods
(Korean Mathematical Society, 2022) Altuntaş, Çağatay; Göral, Haydar; Sertbaş, Doğa Can
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.
Citation - WoS: 1
Citation - Scopus: 1
Applications of Class Numbers and Bernoulli Numbers To Harmonic Type Sums
(Korean Mathematical Society, 2021) Göral, Haydar; Sertbaş, Doğa Can
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.

Mathematics / Matematik