HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

On a theorem of Erdos and Szemeredi

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [8 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01103868
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Thursday, January 15, 2015 - 3:27:06 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Thursday, April 16, 2015 - 10:51:40 AM

File

3Article3.pdf
Explicit agreement for this submission

Identifiers

Collections

Citation

Mangala J Narlikar. On a theorem of Erdos and Szemeredi. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1980, Volume 3 - 1980, pp.41 - 47. ⟨10.46298/hrj.1980.90⟩. ⟨hal-01103868⟩

Share

Metrics

Record views

75

Files downloads

386