On a theorem of Erdos and Szemeredi
Narlikar, Mangala J
HAL, hal-01103868 / Harvested from HAL
Text on HAL
K. F. Roth proved in 1957 that if $1 = q_1 < q_2 \!\!> h,$ where $h \geq x^{\theta}.$ Refining some of Szemeredi's ideas, it is proved in this paper that %if 0 < < 1, and $\sum\frac{1}{b_i}<\infty$, then$$Q(x+h) - Q(x) >\!\!> h,$$where $x\geq h \geq x^{\theta}$ and $\theta >\frac{1}{2}$ is any constant. %In the later part, using the ideas of Jutila, Brun and I. M. Vinogradov, a stronger version (Theorem 2) is proved.
Publié le : 1980-07-04
Classification:  gaps in sequences like square-free integers,  [MATH]Mathematics [math] 
@article{hal-01103868,
     author = {Narlikar, Mangala J},
     title = {On a theorem of Erdos and Szemeredi},
     journal = {HAL},
     volume = {1980},
     number = {0},
     year = {1980},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01103868}
}

Narlikar, Mangala J. On a theorem of Erdos and Szemeredi. HAL, Tome 1980 (1980) no. 0, . http://gdmltest.u-ga.fr/item/hal-01103868/