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SUMMARY:Seoyoung Kim (Queen's University)
DTSTART:20210628T194000Z
DTEND:20210628T203000Z
DTSTAMP:20260419T121031Z
UID:AFDRT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/6/">Fr
 om the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture</a>\nby 
 Seoyoung Kim (Queen's University) as part of Around Frobenius distribution
 s and related topics II\n\n\nAbstract\nLet E be an elliptic curve over Q\,
  and let a_p be the Frobenius trace for each prime p. In 1965\, Birch and 
 Swinnerton-Dyer formulated a conjecture which implies the convergence of t
 he Nagao-Mestre sum\n$lim_{x->infty} (1/log x) \\sum_{p < x}(a_p log p)/p=
 -r+1/2\,$\nwhere r is the order of the zero of the L-function of E at s=1\
 , which is predicted to be the Mordell-Weil rank of E(Q). We show that if 
 the above limit exists\, then the limit equals -r+1/2\, and study the conn
 ections to the Riemann hypothesis for E. We also relate this to Nagao's co
 njecture for elliptic curves. Furthermore\, we discuss a generalization of
  the above results for the Selberg classes and hence (conjecturally) for t
 he L-function of abelian varieties\, and their relations to the generalize
 d Nagao's conjecture. This is a joint work with M. Ram Murty.\n
LOCATION:https://researchseminars.org/talk/AFDRT/6/
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