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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250307T133000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-141
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:HABIBA KADIRI\, UNIVERSITY OF LETHBRIDGE\n\nAn explicit version
  of Chebotarev’s Density Theorem.\n\nThis talk will first provide a (non
 -exhaustive) survey of explicit\nresults on zero-free regions and zero den
 sities of the Riemann zeta\nfunction and their relationship to error terms
  in the prime number\ntheorem. This will be extended to Dirichlet L functi
 ons and Dedekind\nzeta functions\, where new challenges arise with potenti
 al exceptional\nzeros. We will explore estimates for the error terms for p
 rime\ncounting functions across various contexts\, with a specific attenti
 on\nto number fields. Chebotarev’s density theorem states that prime\nid
 eals are equidistributed among the conjugacy classes of the Galois\ngroup 
 of any normal extension of number fields. An effective version\nof this th
 eorem was first established by Lagarias and Odlyzko in 1977.\nIn this arti
 cle\, we present an explicit refinement of their result.\nKey aspects of o
 ur approach include using the following: smoothing\nfunctions\, recently e
 stablished zero-free regions and zero-counting\nformula for zeros of the D
 edekind zeta function\, and sharp bounds for\nBessel-type integrals. This 
 is joint wok with Sourabh Das and Nathan\nNg.\n\nMC 2034
DTSTAMP:20260406T182836Z
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