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UID:5114@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240409T110000
DTEND;TZID=Europe/Paris:20240409T110000
DTSTAMP:20240819T140155Z
URL:https://www.i2m.univ-amu.fr/evenements/on-bounds-for-b_2g-sequences-an
 d-the-erdos-turan-conjecture-javier-pliego-garcia/
SUMMARY:Javier Pliego-Garcia (Univ. Gênes): On bounds for B_{2}[g] sequenc
 es and the Erdos-Turan Conjecture
DESCRIPTION:Javier Pliego-Garcia: We say that Asubset N is an asymptotic ba
 sis 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 t
 he number of such solutions. An old conjecture of Erdos and Turan claims t
 hat there is no asymptotic basis A and no fixed ginmathbb{N} with the prop
 erty 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] |.
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
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