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1
Content available remote

Ramanujan sums and almost periodic functions

100%
Erdös P., Kac M., van Kampen E. R., Wintner A.
Studia Mathematica
|
1940
|
tom 9
|
nr 1
43-53
2
Content available remote

On partitions of lines and space

100%
Erdös P., Jackson S., Daniel Mauldin R.
Fundamenta Mathematicae
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1994
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tom 145
|
nr 2
101-119
EN
We consider a set, L, of lines in $ℝ^n$ and a partition of L into some number of sets: $L = L_1∪...∪ L_p$. We seek a corresponding partition $ℝ^n = S_1 ∪...∪ S_p$ such that each line l in $L_i$ meets the set $S_i$ in a set whose cardinality has some fixed bound, $ω_τ$. We determine equivalences between the bounds on the size of the continuum, $2^ω ≤ ω_θ$, and some relationships between p, $ω_τ$ and $ω_θ$.
3
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On infinite partitions of lines and space

100%
Erdös P., Jackson S., Daniel Mauldin R.
Fundamenta Mathematicae
|
1997
|
tom 152
|
nr 1
75-95
EN
Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
4
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On definite quadratic forms, which are not the sum of two definite or semi-definite forms

74%
Erdös P., Ko C.
Acta Arithmetica
|
1939
|
tom 3
|
nr 1
102-122
5
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Some remarks on subgroups of real numbers

74%
Erdös P.
Colloquium Mathematicum
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1979
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tom 42
|
nr 1
119-120
6
Content available remote

Additive bases with many representations

62%
Erdös P., Nathanson M. B.
Acta Arithmetica
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1989
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tom 52
|
nr 4
399-406
7
Content available remote

Some personal reminiscences of the mathematical work of Paul Turán

62%
Erdös P.
Acta Arithmetica
|
1980
|
tom 37
|
nr 1
3-8
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