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UID:7681@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20161206T140000
DTEND;TZID=Europe/Paris:20161206T150000
DTSTAMP:20241120T204756Z
URL:https://www.i2m.univ-amu.fr/evenements/correlations-of-multiplicative-
 functions-and-applications/
SUMMARY:Oleksiy Klurman (University College London): Correlations of multip
 licative functions and applications
DESCRIPTION:Oleksiy Klurman: We develop the asymptotic formulas for correla
 tions\nΣ{n}≤{x}{f}1({P}1({n})) {f}2({P}2({n})) ... {f}{m}({P}{m}({n}))\
 nwhere {f}1\, ...\, {f}{m} are bounded "pretentious" multiplicative functi
 ons\, under certain natural hypotheses. We then deduce several desirable c
 onsequences: first\, we characterize all multiplicative functions {f}: {{N
 }} → {-1\,+1} with bounded partial sums. This answers a question of Erd
 ős from 1957 in the form conjectured by Tao. Second\, we show that if the
  average of the first divided difference of multiplicative function is zer
 o\, then either {f}({n})={n}{s} for Re({s})&lt\;1 or |{f}({n})| is small o
 n average. This settles an old conjecture of Kátai. Third\, we discuss so
 me recent applications to the study of sign patterns of ({f}({n})\,{f}({n}
 +1)\,{f}({n}+2)) and ({f}({n})\,{f}({n}+1)\,{f}({n}+2)\,{f}({n}+3))} where
  {f}: {{N}} → {-1\,+1} is a given multiplicative function. If time permi
 ts\, we discuss multidimensional version of some of the results mentioned 
 above.\nhttps://arxiv.org/abs/1603.08453\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 016/12/Oleksiy_Klurman.jpg
CATEGORIES:Séminaire,Ernest
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DTSTART:20161030T020000
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