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SUMMARY: Additive problems and exponential sums over smooth numbers - Adam
  Harper (University of Cambridge)
DTSTART:20151201T141500Z
DTEND:20151201T151500Z
UID:TALK61453@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:A number is said to be _y_-smooth if all of its prime factors 
 are at most _y_. Exponential sums over the _y_-smooth numbers less than _x
 _ have been widely investigated\, but existing results were weak for _y_ t
 oo small compared with _x_. For example\, if _y_ is a power of _log x_ the
 n existing results were insufficient to study three variable additive prob
 lems involving smooth numbers (e.g. problems analogous to the three variab
 le Goldbach conjecture)\, except by assuming conjectures like the Generali
 sed Riemann Hypothesis.\n\nI will try to describe my work on bounding mean
  values of exponential sums over smooth numbers\, which allows an uncondit
 ional treatment of three variable additive problems even with _y_ a (large
 ) power of _log x_. There are connections with restriction theory and addi
 tive combinatorics.
LOCATION:MR13
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