Publikationsdatum:
2011-11-24
Beschreibung:
Let A {1, ..., N } and P 1 , ..., P Z[ n ] with P i (0) = 0 and deg P i = k for every 1 ≤ i ≤ . We show, using Fourier analytic techniques, that, for every 〉 0, there necessarily exists n N such that holds simultaneously for 1 ≤ i ≤ (in other words all of the polynomial shifts of the set A intersect A ‘ -optimally’), as long as N ≥ N 1 ( , P 1 , ..., P ). The quantitative bounds obtained for N 1 are explicit but poor; we establish that N 1 may be taken to be a constant (depending only on P 1 , ..., P ) times a tower of 2's of height C * k , + C –2 .
Print ISSN:
0024-6093
Digitale ISSN:
1469-2120
Thema:
Mathematik
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