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Applications of class numbers and Bernoulli numbers to harmonic type sums

Haydar Goral|Doga Can Sertbas
대한수학회 (The Korean Mathematical Society)|2021.11|대한수학회보 (Bulletin of the KMS)|제58권 제6호|pp. 1463-1481|DOI 10.4134/BKMS.b201045

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참고문헌

키워드

Bernoulli numbersHarmonic numbersclass numberregular primes
주제분류수학

초록

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.

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.

참고문헌 (30)

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