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SUMMARY:Seoyoung Kim (Queen's University)
DTSTART:20200810T163000Z
DTEND:20200810T170000Z
DTSTAMP:20260423T021225Z
UID:POINT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/11/">F
 rom the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture</a>\nby
  Seoyoung Kim (Queen's University) as part of POINT: New Developments in N
 umber Theory\n\n\nAbstract\nLet $E$ be an elliptic curve over $\\mathbb{Q}
 $ with discriminant\, and let $a_p$ be the Frobenius trace for each prime 
 p. In 1965\, Birch and Swinnerton-Dyer formulated a conjecture which impli
 es\n\n$\\lim\\limits_{x \\rightarrow \\infty} \\frac{1}{\\log x} \\sum_{p<
  x} \\frac{a_p\\log p}{p}=-r+\\frac{1}{2}\,$\n\nwhere $r$ is the order of 
 the zero of the $L$-function of $E$ at $s=1$\, which is predicted to be th
 e Mordell-Weil rank of $E(\\mathbb{Q})$. We show that if the above limit e
 xits\, then the limit equals $-r+\\frac{1}{2}$\, and study the connections
  to Riemann hypothesis for $E$. We also relate this to Nagao's conjecture.
  This is a recent joint work with M. Ram Murty.\n\nPlease register for the
  talks on August 10 here:\nhttps://fordham.zoom.us/meeting/register/tJwpde
 2srTgqHdYG6NMu5WmgzPiDnNJQMTsM\n
LOCATION:https://researchseminars.org/talk/POINT/11/
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