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SUMMARY:On a problem of J.E. Littlewood on flat polynomials - Julian Sahas
 rabudhe (University of Cambridge)
DTSTART:20191016T124500Z
DTEND:20191016T134500Z
UID:TALK132322@talks.cam.ac.uk
CONTACT:Thomas Bloom
DESCRIPTION:A polynomial is said to be a Littlewood polynomial if all of i
 ts coefficients are either +1 or -1. Erdos\, in 1957\, asked how `flat' su
 ch polynomials can be on the unit circle. In particular\, he asked if ther
 e exist infinitely many Littlewood polynomials for which \n\\[ c_1 \\leq \
 \frac{\\max_{|z|=1} |f(z)|}{\\min_{|z|=1 } |f(z)| } \\leq c_2\, \\]\nwhere
  $c_1\,c_2 >0 $ are absolute constants. Later\, in 1966\, Littlewood conje
 ctured that such polynomials should indeed exist. \n\nIn this talk I will 
 discuss how combinatorial and probabilistic ideas can be used to resolve t
 his conjecture. This talk is based on joint work with Paul Balister\, Bela
  Bollobas\, Rob Morris and Marius Tiba.
LOCATION:MR5\, CMS
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