Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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APPLICATIONS OF CLASS NUMBERS AND BERNOULLI NUMBERS TO HARMONIC TYPE SUMS

  • Goral, Haydar (Department of Mathematics Izmir Institute of Technology) ;
  • Sertbas, Doga Can (Department of Mathematics Faculty of Science Cukurova University)
  • Received : 2020.12.15
  • Accepted : 2021.04.06
  • Published : 2021.11.30
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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.

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References

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