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SUMMARY:Tian Wang (University of Illinois at Chicago)
DTSTART:20210629T180000Z
DTEND:20210629T185000Z
DTSTAMP:20260419T121654Z
UID:AFDRT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AFDRT/9/">Bo
 unds for the distribution of the Frobenius traces associated to products o
 f non-CM elliptic curves</a>\nby Tian Wang (University of Illinois at Chic
 ago) as part of Around Frobenius distributions and related topics II\n\n\n
 Abstract\nLet $A/\\mathbb{Q}$ be an abelian variety that is isogenous over
  $\\mathbb{Q}$ to the product $E_1 \\times \\ldots \\times E_g$ of ellipti
 c curves $E_1/\\mathbb{Q}$\, $\\ldots$\, $E_g/\\mathbb{Q}$ without complex
  multiplication and pairwise non-isogenous over $\\overline{\\mathbb{Q}}$.
  For an  integer $t$ and a positive real number $x$\, denote by $\\pi_A(x\
 , t)$ the number of primes $p \\leq x$\, of good reduction for the abelian
  variety $A$\, for which the Frobenius trace associated to the reduction o
 f $A$ modulo $p$ equals $t$.\n\nBased on prior approaches to the Lang-Trot
 ter Conjecture for the Frobenius traces associated to reduction of \n\nan 
 elliptic curve\, under the RH and the GRH for  Dedekind zeta functions\, w
 e prove a non-trivial upper bound for $\\pi_A(x\, t)$.\n\nThis is joint wo
 rk with Alina Carmen Cojocaru.\n
LOCATION:https://researchseminars.org/talk/AFDRT/9/
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