Répartition simultanée de S(n) et S(n+1) dans les progressions arithmétiques

Abstract : If q≥2 is an integer, we denote by Sq(n) the sum of the digits in base q of the positive integer n and by vq(n) its q-adic valuation. The goal of this work is to study exponential sums of the form ∑n≤xexp(2iπ(lmSq(n)+km′Sq(n+1)+θn)) in order to prove some statistical properties of integers n for which Sq(n) and Sq(n+1) belong to given arithmetic progressions. This extends the results obtained by Gelfond in 1968 and those obtained by Mauduit–Sárközy in 1996.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01272915
Contributor : Aigle I2m <>
Submitted on : Thursday, February 11, 2016 - 3:31:08 PM
Last modification on : Monday, March 4, 2019 - 2:04:19 PM

Identifiers

Collections

Citation

Karam Aloui, Christian Mauduit, Mohamed Mkaouar. Répartition simultanée de S(n) et S(n+1) dans les progressions arithmétiques. Ramanujan Journal, Springer Verlag, 2017, 42 (1), pp.173-197. ⟨10.1007/s11139-015-9708-6⟩. ⟨hal-01272915⟩

Share

Metrics

Record views

168