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CATEGORIES:Number Theory Seminar
SUMMARY: Additive problems and exponential sums over smoot
h numbers - Adam Harper (University of Cambridge)
DTSTART;TZID=Europe/London:20151201T141500
DTEND;TZID=Europe/London:20151201T151500
UID:TALK61453AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61453
DESCRIPTION:A number is said to be _y_-smooth if all of its pr
ime factors are at most _y_. Exponential sums over
the _y_-smooth numbers less than _x_ have been wi
dely investigated\, but existing results were weak
for _y_ too small compared with _x_. For example\
, if _y_ is a power of _log x_ then existing resul
ts were insufficient to study three variable addit
ive problems involving smooth numbers (e.g. proble
ms analogous to the three variable Goldbach conjec
ture)\, except by assuming conjectures like the Ge
neralised Riemann Hypothesis.\n\nI will try to des
cribe my work on bounding mean values of exponenti
al sums over smooth numbers\, which allows an unco
nditional treatment of three variable additive pro
blems even with _y_ a (large) power of _log x_. Th
ere are connections with restriction theory and ad
ditive combinatorics.
LOCATION:MR13
CONTACT:Jack Thorne
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