Comptes Rendus
Number theory
Small values of signed harmonic sums
Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1062-1074.

For every τR and every integer N, let mN(τ) be the minimum of the distance of τ from the sums n=1Nsn/n, where s1,,sn{1,+1}. We prove that mN(τ)<exp(C(logN)2), for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than 1/log4.

Pour tout τR et tout entier N, soit mN(τ) la distance minimale de τ aux sommes n=1Nsn/n, où s1,,sn{1,+1}. On montre que mN(τ)<exp(C(logN)2) pour tout entier positif N suffisamment grand (dépendant de C et τ), quelle que soit la constante positive C, inférieure à 1/log4.

Published online:
DOI: 10.1016/j.crma.2018.11.007

Sandro Bettin 1; Giuseppe Molteni 2; Carlo Sanna 3

1 Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
2 Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy
3 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
     author = {Sandro Bettin and Giuseppe Molteni and Carlo Sanna},
     title = {Small values of signed harmonic sums},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1062--1074},
     publisher = {Elsevier},
     volume = {356},
     number = {11-12},
     year = {2018},
     doi = {10.1016/j.crma.2018.11.007},
     language = {en},
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Sandro Bettin; Giuseppe Molteni; Carlo Sanna. Small values of signed harmonic sums. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1062-1074. doi : 10.1016/j.crma.2018.11.007.

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