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SUMMARY:Do the zeros of one $L$-function know about the others? [MPIM]
DTSTART:20260819T123000Z
DTEND:20260819T133000Z
DTSTAMP:20260822T032500Z
UID:indico-event-1539@math-events.uni-bonn.de
DESCRIPTION:Speakers: William D. Banks (University of Missouri)\n\nNumber 
 theory lunch seminar\nIn principle\, the zeros of two distinct Dirichlet $
 L$-functions oughtto be unrelated. In fact\, they turn out to be far more 
 entangled than one expects\, though not always.  My talk will survey some
  recent results in this circle of ideas\, including Linnik--Sprind\\v{z}uk
 -type equivalences that reduce GRH to the vertical distribution of the zer
 os of a single $L$-function.  I will also describe in greater depth some 
 joint work with Kyle Loftus evaluating the twisted moment $\\sum_{\\rho} x
 ^{\\rho} L(\\rho\,\\chi_1)$ over the zeros $\\rho$ of a second $L$-functio
 n $L(s\,\\chi_2)$. Our results are unconditional and hold in short windows
 \, and they imply that no nontrivial linear combination of Dirichlet $L$-f
 unctions vanishes on the entire zero set of another. \n\nhttps://math-eve
 nts.uni-bonn.de/event/1539/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1539/
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