On an Application of Higher Energies to Sidon Sets
We show that for any finite set A and an arbitrary ε > 0 there exists k = k ( ε ) such that the higher energy E k ( A ) is at most | A | k + ε unless A has a very specific structure. As an application we obtain that any finite subset A of the real numbers or the prime field either contains an add...
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| Veröffentlicht in: | Combinatorica (Budapest. 1981) 2023-04, Vol.43 (2), p.329-345 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that for any finite set
A
and an arbitrary
ε
>
0
there exists
k
=
k
(
ε
)
such that the higher energy
E
k
(
A
)
is at most
|
A
|
k
+
ε
unless
A
has a very specific structure. As an application we obtain that any finite subset
A
of the real numbers or the prime field either contains an additive Sidon-type subset of size
|
A
|
1
/
2
+
c
or a multiplicative Sidon-type subset of size
|
A
|
1
/
2
+
c
. |
|---|---|
| ISSN: | 0209-9683 1439-6912 |
| DOI: | 10.1007/s00493-023-00013-y |