On the Asymptotic Behaviour of the Integral T(x)=∫0+∞|{xt}−{xt+1}|dt T(x)=\int_0^{+\infty}\left|\left\{\frac{x}{t}\right\}-\left\{\frac{x}{t+1}\right\}\right|\,dt
By: Mihoub Bouderbala and Meselem Karras
References
- APOSTOL, T. M.: Introduction to Analytic Number Theory. Springer-Verlag, 1976.
- BALAZARD, M.: Sur la variation totale de la suite des parties fractionnaires des quotients d’un nombre réel positif par les nombres entiers naturels consécutifs, Mosc. J. Comb. Number Theory 7 (2017), 3–23.
- BALAZARD, M.—BENFERHAT, L.—BOUDERBALA, M.: Sur la variation de certaines suites de parties fractionnaires, Commun. in Math. 29 (2021), no. 3, 407–430.
- BOURGAIN, J.—WATT, N.: Mean square of zeta function, circle problem and divisor problem revisited, Preprint (2017), arXiv:1709.04340.
- [5]
MERCIER, A.—NOWAK, W. G.: On the asymptotic behaviour of sums
∑_{n≤x} g(n){x/n}^k - WINTNER, A.: Square root estimates of arithmetical sum functions, Duke Math. J. 13 (1946), 185–193.
- [7]
WU, L.—SHI, S.: On the asymptotic behavior of sums
∑_{n≤x} f(n){x/n}^k
Language: English
Page range: 119 - 132
Submitted on: Feb 23, 2026
Accepted on: Jun 25, 2026
Published on: Jun 30, 2026
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Related subjects:
© 2026 Mihoub Bouderbala, Meselem Karras, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.