Geodesic
On the variation of certain fractional part sequences
Communications in Mathematics, Tome 29 (2021) no. 3, pp. 407-430.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $b>a>0$. We prove the following asymptotic formula $$ \sum _{n\geqslant 0} \big \lvert \{x/(n+a)\}-\{x/(n+b)\}\big \rvert =\frac {2}{\pi }\zeta (3/2)\sqrt {cx}+O(c^{2/9}x^{4/9})\,, $$ with $c=b-a$, uniformly for $x \geqslant 40 c^{-5}(1+b)^{27/2}$.
Classification : 11N37
Keywords: Fractional part; Elementary methods; van der Corput estimates 
@article{COMIM_2021__29_3_a6,
     author = {Balazard, Michel and Benferhat, Leila and Bouderbala, Mihoub},
     title = {On the variation of certain fractional part sequences},
     journal = {Communications in Mathematics},
     pages = {407--430},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2021},
     mrnumber = {4355415},
     zbl = {07484377},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a6/}
}
TY  - JOUR
AU  - Balazard, Michel
AU  - Benferhat, Leila
AU  - Bouderbala, Mihoub
TI  - On the variation of certain fractional part sequences
JO  - Communications in Mathematics
PY  - 2021
SP  - 407
EP  - 430
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a6/
LA  - en
ID  - COMIM_2021__29_3_a6
ER  - 
%0 Journal Article
%A Balazard, Michel
%A Benferhat, Leila
%A Bouderbala, Mihoub
%T On the variation of certain fractional part sequences
%J Communications in Mathematics
%D 2021
%P 407-430
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a6/
%G en
%F COMIM_2021__29_3_a6
Balazard, Michel; Benferhat, Leila; Bouderbala, Mihoub. On the variation of certain fractional part sequences. Communications in Mathematics, Tome 29 (2021) no. 3, pp. 407-430. http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a6/