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SUMMARY:Trevor Dion Wooley (Purdue University)
DTSTART:20260715T193000Z
DTEND:20260715T202000Z
DTSTAMP:20260710T111638Z
UID:CANT2026/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/40/
 ">Strong paucity in systems of diagonal equations</a>\nby Trevor Dion Wool
 ey (Purdue University) as part of Combinatorial and additive number theory
  seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduat
 e Center (4th floor).\n\nAbstract\nLet $k$ be a natural number with $k\\ge
  2$\, and let $\\varepsilon>0$. We consider the number\n$V_k^*(P)$ of inte
 gral solutions of the system of simultaneous Diophantine equations $$x_1^{
 2j-1}+\\ldots +x_{k+1}^{2j-1}=y_1^{2j-1}+\\ldots +y_{k+1}^{2j-1}\\quad (1\
 \le j\\le k).$$ with $1\\le x_i\,y_i\\le P$ $(1\\le i\\le k+1)$. Writing $
 L_k^*(P)$ for the number of diagonal solutions with \n$\\{x_1\,\\ldots \,x
 _{k+1}\\}=\\{y_1\,\\ldots \,y_{k+1}\\}$\, so that $L_k^*(P)\\sim (k+1)!P^{
 k+1}$\, we prove that $$V_k^*(P)-L_k^*(P)\\ll P^{\\sqrt{8k+9}-1+\\varepsil
 on}.$$ This establishes a strong paucity result improving on earlier work 
 of Brüdern and Robert. Time permitting\, we describe analogous results fo
 r related problems.\n
LOCATION:https://researchseminars.org/talk/CANT2026/40/
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