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SUMMARY:Cihan Sabuncu (Universite de Montreal)
DTSTART:20250523T153000Z
DTEND:20250523T155500Z
DTSTAMP:20260423T041653Z
UID:CANT2025/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/63/
 ">Extreme values of $r_3(n)$ in arithmetic progressions</a>\nby Cihan Sabu
 ncu (Universite de Montreal) as part of Combinatorial and additive number 
 theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Cente
 r (4th floor).\n\nAbstract\nA classical result of Chowla shows that the re
 presentation function $r_3(n)$\, which counts the number of ways $n$ can b
 e expressed as a sum of three squares\, satisfies $$r_3(n) \\gg \\sqrt{n} 
 \\log\\log n $$ \nfor infinitely many integers $n$. This lower bound\, in 
 turn\, also implies that $ L(1\, \\chi_D) \\gg \\log\\log |D|$ holds for i
 nfinitely many fundamental discriminants $D<0$. In this talk\, we will inv
 estigate whether such extremal behavior of $r_3(n)$ persists when $n$ is r
 estricted to lie in an arithmetic progression $n\\equiv a \\pmod q$. \\\\T
 his is joint work with Jonah Klein and Michael Filaseta.\n
LOCATION:https://researchseminars.org/talk/CANT2025/63/
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