On $B_{2k}$-sequences

Martin Helm. "On $B_{2k}$-sequences." Acta Arithmetica 63.4 (1993): 367-371. <http://eudml.org/doc/206528>.

@article{MartinHelm1993,
abstract = {Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a $B_r$-sequence A satisfies $lim inf_\{n→ ∞\} (A(n)/(n^\{1/r\}))=0$. The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof of Erdős’ hypothesis for all even r=2k which we developped independently of Jia’s version.},
author = {Martin Helm},
journal = {Acta Arithmetica},
keywords = {-sequence; Sidon sets},
language = {eng},
number = {4},
pages = {367-371},
title = {On $B_\{2k\}$-sequences},
url = {http://eudml.org/doc/206528},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Martin Helm
TI - On $B_{2k}$-sequences
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 4
SP - 367
EP - 371
AB - Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a $B_r$-sequence A satisfies $lim inf_{n→ ∞} (A(n)/(n^{1/r}))=0$. The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof of Erdős’ hypothesis for all even r=2k which we developped independently of Jia’s version.
LA - eng
KW - -sequence; Sidon sets
UR - http://eudml.org/doc/206528
ER -