Répartition simultanée de m class="a-plus-plus">Sm>(m class="a-plus-plus">nm>) et d-i-eq1"> mat-t-e-x" xmlns:search="http://marklogic.com/appservices/search">\(S(n+1)\) dans les progressions arithmétiques

详细信息    查看全文

• 作者：Karam Aloui ; Christian Mauduit ; Mohamed Mkaouar
• 关键词：Mots clésSomme des chiffres ; Sommes exponentielles ; Théorème d’Erdös ; Kac
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：42
• 期：1
• 页码：173-197
• 全文大小：<len>
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

If \(q\ge 2\) is an integer, we denote by \(S_q(n)\) the sum of the digits in base q of the positive integer n and by \(v_q(n)\) its q-adic valuation. The goal of this work is to study exponential sums of the form \(\displaystyle \sum \nolimits _{n\le x}\exp \big (2i\pi \big (\frac{l}{m} S_q(n)+\frac{k}{m'}S_q(n+1)+\theta n\big )\big )\) in order to prove some statistical properties of integers n for which \(S_q(n)\) and \(S_q(n+1)\) belong to given arithmetic progressions. This extends the results obtained by Gelfond in 1968 and those obtained by Mauduit–Sárközy in 1996.