| Tartalom: |
http://real.mtak.hu/65700/ |
| Archívum: |
MTA Könyvtár |
| Gyûjtemény: |
Status = Published
Type = Article
|
| Cím: |
An improvement of a theorem of Erdős and Sárközy
|
| Létrehozó: |
Horváth, Gábor
|
| Kiadó: |
Akadémiai Kiadó
|
| Dátum: |
2007
info:eu-repo/date/embargoEnd/2027-12-31
|
| Téma: |
TA Engineering (General). Civil engineering (General) / általános mérnöki tudományok
|
| Tartalmi leírás: |
Let
a
<sub>1</sub>
<
a
<sub>2</sub>
< … be an infinite sequence of positive integers and denote by
R
<sub>2</sub>
(
n
) the number of solutions of
n
=
a
<sub>i</sub>
+
a
<sub>j</sub>
. P. Erdős and A. Sárközy proved that if
g
(
n
) is a monotonically increasing arithmetic function with
g
(
n
) → +∞ and
g
(
n
) =
o
(
n
(log
n
)
<sup>−2</sup>
) then |
R
<sub>2</sub>
(
n
) −
g
(
n
)| =
o
(√
g
(
n
)) cannot hold. We will show that for any
É›
> 0, the inequality |
R
<sub>2</sub>
(
n
) −
g
(
n
)| ≤ (1 −
É›
)√
g
(
n
) cannot hold from a certain point on.
|
| Nyelv: |
magyar
|
| Típus: |
Article
PeerReviewed
info:eu-repo/semantics/article
|
| Formátum: |
text
|
| Azonosító: |
Horváth, Gábor (2007) An improvement of a theorem of Erdős and Sárközy. Pollack Periodica, 2 (Supple). pp. 155-161. ISSN 1788-1994
|
| Kapcsolat: |
https://doi.org/10.1556/Pollack.2.2007.S.14
|
| Létrehozó: |
info:eu-repo/semantics/embargoedAccess
|
