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UID:6958@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191007T100000
DTEND;TZID=Europe/Paris:20191007T110000
DTSTAMP:20241120T202635Z
URL:https://www.i2m.univ-amu.fr/evenements/the-wiener-spectrum-and-taylor-
 series-with-pseudo-random-coefficients/
SUMMARY: ‪Mikhail Sodin (Tel Aviv University\, Israel): The Wiener spectr
 um and Taylor series with pseudo-random coefficients
DESCRIPTION: ‪Mikhail Sodin: The theme of my talk will be the influence o
 f the multipliers ξ(n) on the angular distribution of zeroes of the Taylo
 r series  This is a classical topic initiated by Littlewood together with 
 his pupils and collaborators Chen\, Nassif\, and Offord. Our main finding 
 is that the leading term in the asymptotic behaviour of log |Fξ(z)| (and 
 hence\, the distribution of zeroes of Fξ) is governed by the Wiener spect
 rum of the sequence ξ\, that is\, by the support of spectral measure of 
 ξ. It applies to random stationary sequences\, to the sequences ξ(n) = e
 xp(nβ) with non-integer β &gt\; 1 and ξ(n) = exp(Q(n))\, where Q is a W
 eyl polynomial\, to Besicovitch almost periodic sequences\, to multiplicat
 ive random sequences\, and to the Möbius function (assuming “the binary
  Chowla conjecture”). The talk will be based on the joint works with Jac
 ques Benatar\, Alexander Borichev\, and Alon Nishry (arXiv:1409.2736\, 190
 8.09161).\n&nbsp\;\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/03/Mikhail_Sodin.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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