On bounds for B_{2}[g] sequences and the Erdos-Turan Conjecture
Javier Pliego-Garcia
Univ. Gênes
Date(s) : 09/04/2024 iCal
11h00
We say that Asubset 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 ginmathbb{N} with the property that 1leq 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 ggeq 2 and some sequence Asubset N with the property that r_{A}(m)leq g new lower bounds for the counting function | A cap [1,x] |.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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