Let be the set of all positive integers such that the denominator of is less than the least common multiple of . In this paper, under a certain assumption on linear independence, we prove that the set has the upper asymptotic density . The assumption follows from Schanuel’s conjecture.
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Keywords: harmonic numbers, least common multiples, upper asymptotic density
Bing-Ling Wu 1; Xiao-Hui Yan 2
@article{CRMATH_2022__360_G1_53_0, author = {Bing-Ling Wu and Xiao-Hui Yan}, title = {On the denominators of harmonic numbers. {IV}}, journal = {Comptes Rendus. Math\'ematique}, pages = {53--57}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.282}, language = {en}, }
Bing-Ling Wu; Xiao-Hui Yan. On the denominators of harmonic numbers. IV. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 53-57. doi : 10.5802/crmath.282. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.282/
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