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SUMMARY:Youness Lamzouri (IECL (Université de Lorraine))
DTSTART:20211020T150000Z
DTEND:20211020T160000Z
DTSTAMP:20260423T052956Z
UID:hnts/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/39/">Ze
 ros of linear combinations of L-functions near the critical line</a>\nby Y
 ouness Lamzouri (IECL (Université de Lorraine)) as part of Heilbronn numb
 er theory seminar\n\nLecture held in 2.04 Fry building\, University of Bri
 stol.\n\nAbstract\nIn this talk\, I will present a recent joint work with 
 Yoonbok Lee\, where we investigate the number of zeros of linear combinati
 ons of $L$-functions in the vicinity of the critical line. More precisely\
 , we let $L_1\, \\dots\, L_J$ be distinct primitive $L$-functions belongin
 g to a large class (which conjecturally contains all $L$-functions arising
  from automorphic representations on $\\text{GL}(n)$)\, and $b_1\, \\dots\
 , b_J$ be real numbers. Our main result is an asymptotic formula for the n
 umber of zeros of $F(\\sigma+it)=\\sum_{j\\leq J} b_j L_j(\\sigma+it)$ in 
 the region $\\sigma\\geq 1/2+1/G(T)$ and $t\\in [T\, 2T]$\, uniformly in t
 he range $\\log \\log T \\leq G(T)\\leq (\\log T)^{\\nu}$\, where $\\nu\\a
 symp 1/J$. This establishes a general form of a conjecture of Hejhal in th
 is range. The strategy of the proof relies on comparing the distribution o
 f $F(\\sigma+it)$ to that of an associated probabilistic random model.\n
LOCATION:https://researchseminars.org/talk/hnts/39/
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