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SUMMARY:Polynomial bounds for Chowla's cosine problem - Benjamin Bedert (U
 niversity of Cambridge)
DTSTART:20251126T133000Z
DTEND:20251126T143000Z
UID:TALK237823@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION:Inspired by investigations of zeta functions\, and old problem
  of Ankeny and Chowla asks whether any cosine polynomial f_A(x)=cos(a_1 x)
 + ... +cos(a_n x)\, for an arbitrary set A={a_1\,...a_n} of n distinct pos
 itive integers\, must take a large negative value for some x in [0\,2 pi].
  Chowla later conjectured that the largest negative value of f_A is always
  at least of order n^1/2^\, for any set A of size n. A refinement of Bourg
 ain's approach due to Ruzsa gave the previous record bound of exp(sqrt(log
  n)). In this talk\, we discuss recent progress establishing the first pol
 ynomial bound n^c^ with exponent c=1/7. We remark that Jin\, Milojevic\, T
 omon and Zhang independently proved a polynomial bound with exponent c app
 roximately 1/100 using a different method.\n
LOCATION:MR4\, CMS
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