BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Alexandre de Faveri (California Institute of Technology)
DTSTART:20211124T160000Z
DTEND:20211124T170000Z
DTSTAMP:20260423T021432Z
UID:hnts/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/43/">Si
 mple zeros of GL(2) L-functions</a>\nby Alexandre de Faveri (California In
 stitute of Technology) as part of Heilbronn number theory seminar\n\nLectu
 re held in 2.04 Fry.\n\nAbstract\nI will discuss my recent work on simple 
 zeros of automorphic L-functions of degree 2. For a primitive holomorphic 
 form $f$ of arbitrary weight and level\, I show that its completed L-funct
 ion has $\\Omega(T^\\delta)$ simple zeros with imaginary part in $[-T\, T]
 $\, for any $\\delta < \\frac{2}{27}$. This provides the first power bound
  in this problem for $f$ of non-trivial level\, where the previous best bo
 und was $\\Omega(\\log \\log \\log T)$. The proof uses a method of Conrey-
 Ghosh combined with ideas of Booker and Booker-Milinovich-Ng\, in addition
  to a new ingredient coming from zero-density estimates for twists of $f$.
  I will explain the basic method\, the obstructions that arise when $f$ ha
 s non-trivial level\, and how to unconditionally get around such obstructi
 ons to obtain a power bound. This argument gives a curious connection betw
 een the quality of zero-density estimates for a certain family and the num
 ber of simple zeros for a single element of that family.\n
LOCATION:https://researchseminars.org/talk/hnts/43/
END:VEVENT
END:VCALENDAR