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2 results on '"harmonic numbers"'

1. On the denominators of harmonic numbers. IV

Author

Wu, Bing-Ling and Yan, Xiao-Hui

Subjects
harmonic numbers, least common multiples, upper asymptotic density, Mathematics, QA1-939
Abstract

Let $\mathcal{L}$ be the set of all positive integers $n$ such that the denominator of $1+1/2+\cdots +1/n$ is less than the least common multiple of $1, 2, \dots , n$. In this paper, under a certain assumption on linear independence, we prove that the set $\mathcal{L}$ has the upper asymptotic density $1$. The assumption follows from Schanuel’s conjecture.

Published
2022
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2. Nouvelles relations de réciprocité entre sommes d'Euler

Author

Coppo, Marc-Antoine, Candelpergher, Bernard, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Ramanujan summation, harmonic numbers, Cauchy numbers of the first kind, digamma function, Euler sums, Ramanujan summation of series, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], zeta values
Abstract

In this study, we apply the Ramanujan summation method to linear Euler sums. This enables us to establish new reflection formulas for these sums that complete results already achieved in our previous works.; Dans cette étude, on applique le procédé de sommation de Ramanujan aux sommes d'Euler linéaires. Ceci nous permet d'établir de nouvelles relations de réciprocité entre sommes d'Euler parachevant les résultats déjà obtenus dans des travaux antérieurs.

Published
2020

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