Sur la variation de certaines suites de parties fractionnaires

Michel Balazard, Leila Benferhat, Mihoub Bouderbala

Let $b>a>0$. We prove the following asymptotic formula $$\sum _{n\ge 0}|\{x/(n+a)\}-\{x/(n+b)\}|=\frac{2}{\pi }\zeta (3/2)\sqrt{cx}+O(c^{2/9}{x}^{4/9}),$$ with $c=b…