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DTSTART:20230312T070000
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DTSTART;TZID=America/Toronto:20231107T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-104
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:SUN WOO PARK\, UNIVERSITY OF WISCONSIN-MADISON\n\n\"ON THE PRIM
 E SELMER RANKS OF CYCLIC PRIME TWIST FAMILIES OF ELLIPTIC\nCURVES OVER GLO
 BAL FUNCTION FIELDS\"\n\nFix a prime number $p$. Let $\\mathbb{F}_q$ be a 
 finite field of\ncharacteristic coprime to 2\, 3\, and $p$\, which also co
 ntains the\nprimitive $p$-th root of unity $\\mu_p$. Based on the works by
 \nSwinnerton-Dyer\, Klagsbrun\, Mazur\, and Rubin\, we prove that the\npro
 bability distribution of the sizes of prime Selmer groups over a\nfamily o
 f cyclic prime twists of non-isotrivial elliptic curves over\n$\\mathbb{F}
 _q(t)$ satisfying a number of mild constraints conforms to\nthe distributi
 on conjectured by Bhargava\, Kane\, Lenstra\, Poonen\, and\nRains with exp
 licit error bounds. The key tools used in proving these\nresults are the R
 iemann hypothesis over global function fields\, the\nErd\\\"os-Kac theorem
 \, and the geometric ergodicity of Markov chains.  \n\nMC 5501
DTSTAMP:20260505T200502Z
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