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Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi

100%

Deshouillers J.-M., Hennecart F., Landreau B.

Acta Arithmetica

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1998

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tom 85

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nr 1

13-33

EN

Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of Hooley on the average of the square of the number of representations.

2

Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture

100%

Deshouillers J.-M., Drmota M., Müllner C.

Studia Mathematica

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2015

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tom 231

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nr 1

83-95

EN

We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.

3

Lois de répartition des diviseurs, 1

87%

Deshouillers J.-M., Dress F., Tenenbaum G.

Acta Arithmetica

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1977-1979

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tom 34

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nr 4

273-285

4

Un problème binaire en théorie additive

62%

Deshouillers J.-M.

Acta Arithmetica

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1973-1974

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tom 25

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nr 4

393-403

Ograniczanie wyników

3 Acta Arithmetica

1 Studia Mathematica

4 Deshouillers J.-M.

1 Dress F.

1 Drmota M.

1 Hennecart F.

1 Landreau B.

1 Müllner C.

1 Tenenbaum G.

1 2015

1 1998

1 1979

1 1974

Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi

Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture

Lois de répartition des diviseurs, 1

Un problème binaire en théorie additive