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SUMMARY:The pair correlation method of zeros of the Riemann zeta-function 
 and the Alternative Hypothesis\, without RH [MPIM]
DTSTART:20250911T130000Z
DTEND:20250911T140000Z
DTSTAMP:20260420T152000Z
UID:indico-event-621@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ade Irma Suriajaya\, Junghun Lee (Kyushu University/
 MPIM)\n\nNumber theory lunch seminar\nMontgomery (1973) suggested an appro
 ach to study the pair correlation of nontrivial zeros of the Riemann zeta-
 function\, and proved the corresponding asymptotic formula within a limite
 d range assuming the Riemann Hypothesis (RH). The extended behavior remain
 s a conjecture which implies the famous Pair Correlation Conjecture (PCC) 
 for these zeros. In Suriajaya's previous work with Siegfred Alan C. Baluyo
 t\, Daniel Alan Goldston\, and Caroline L. Turnage-Butterbaugh\, they have
  showed how to remove RH in such pair correlation methods and recover Mont
 gomery results on the proportion of simple zeros under hypotheses weaker t
 han RH. They have in addition obtained the proportion of zeros lying on th
 e critical line\, which we simply call critical zeros for brevity.    In
  a follow-up work with Daniel Goldston and Jordan Schettler\, we showed th
 at PCC without RH implies that asymptotically 100% of the zeros are simple
  and critical\, thus RH is asymptotically true. Our method applies to othe
 r pair correlation conjectures as well\, such as the Alternative Hypothesi
 s (AH). AH first arose as a consequence of the possible existence of Landa
 u-Siegel zeros of real Dirichlet L-functions\, as demonstrated by D. R. He
 ath-Brown at a 1996 AIM conference. In this talk we would like to introduc
 e the main ideas behind our results.\n\nhttps://math-events.uni-bonn.de/ev
 ent/621/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/621/
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