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SUMMARY:Akshaa Vatwani (IIT Gandhinagar)
DTSTART:20200515T110000Z
DTEND:20200515T120000Z
DTSTAMP:20260423T052930Z
UID:NTdL/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTdL/3/">Log
 arithmic mean values of multiplicative functions</a>\nby Akshaa Vatwani (I
 IT Gandhinagar) as part of Number theory during lockdown\n\n\nAbstract\nA 
 general mean-value theorem for multiplicative functions taking values in t
 he unit disc was given by Wirsing (1967) and Halász (1968). We consider a
  multiplicative function f belonging to a certain class of arithmetical fu
 nctions and let F(s) be the associated Dirichlet series. In this setting\,
  we obtain new Halász-type results for the logarithmic mean value of f. M
 ore precisely\, we give estimates in terms of the size of $|F(1+1/\\log x)
 |$ and show that these estimates are sharp.  As a consequence\, we obtain 
 a non-trivial zero-free region for partial sums of L-functions belonging t
 o our class. \nWe also report on some recent work showing that this zero f
 ree region is optimal. This is joint work with Arindam Roy (UNC Charlotte)
 .\n
LOCATION:https://researchseminars.org/talk/NTdL/3/
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