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SUMMARY:Akos Magyar (University of Georgia)
DTSTART:20260714T153000Z
DTEND:20260714T165500Z
DTSTAMP:20260710T111702Z
UID:CANT2026/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/25/
 ">Almost primes solutions to forms of odd degrees in many variables</a>\nb
 y Akos Magyar (University of Georgia) as part of Combinatorial and additiv
 e number theory seminar (CANT 2026)\n\nLecture held in Science Center in t
 he CUNY Graduate Center (4th floor).\n\nAbstract\nLet $\\mathcal{F}=\\{f_1
 \,\\ldots\,f_R\\}$ be a family of forms of odd degrees at most $d$ in $s$ 
 variables. We study the solutions to the diophantine system: $f_1(\\mathbf
 {x})=\\ldots=f_R(\\mathbf{x})=0$ of the form $x_i=y_ip_i$ with $|y_i|\\leq
  Y_\\mathcal{F}$ and $p_i$ being a prime for all $i\\in [s]$ inside the bo
 x $[-N\,N]^s$\, for large $N$. We show that if the number of variables $s$
  is sufficiently large with respect to the parameters $R$ and $d$\, then t
 here are at least $C_\\mathcal{F} N^{s-D}/(\\log\\\,N)^s$ such solutions f
 or some constants $C_\\mathcal{F}>0$ and $D\\in\\mathbb{N}$\, with $D$ dep
 ending only on the initial parameters $R$ and $d$.\n
LOCATION:https://researchseminars.org/talk/CANT2026/25/
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