Javier Pliego-Garcia
Université de Gênes (Italie)
Date(s) : 09/04/2024 iCal
11 h 00 min
We say that A\subset N is an asymptotic basis of order 2 if for every sufficiently large natural number n then n=a_{1}+a_{2}, a_{1}\leq a_{2}, a_{1},a_{2}\in A, and denote by r_{A}(n) to the number of such solutions. An old conjecture of Erdos and Turan claims that there is no asymptotic basis A and no fixed g\in\mathbb{N} with the property that 1\leq r_{A}(n)\leq g for sufficiently large n. We first show after suitably weakening the preceding requirements in the conjecture that the corresponding statement does not hold. We also provide for g\geq 2 and some sequence A\subset N with the property that r_{A}(m)\leq g new lower bounds for the counting function | A \cap [1,x] |.
Emplacement
Site Sud, Luminy, TPR2, Salle de Séminaire 304-306 (3ème étage)
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