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SUMMARY:Exponential sums over smooth numbers
DTSTART:20150128T110000
DTEND:20150128T120000
DTSTAMP:20260406T194553Z
UID:e840aea8a0feb3f97efbdbfc2f7ca7d2e9aa6336373edd2db8a01c2b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Adam Harper\nAbstrait: A number is said to be $y$-smooth if al
 l of its prime factors are at most $y$. Exponential sums over the $y$-smoo
 th numbers less than $x$ have been widely investigated\, but existing resu
 lts were weak if $y$ is too small compared with $x$. For example\, if $y$ 
 is a power of $\\log x$ then existing results were insufficient to study t
 ernary additive problems involving smooth numbers\, except by assuming con
 jectures like the Generalised Riemann Hypothesis.\nI will try to describe 
 my recent work on bounding mean values of exponential sums over smooth num
 bers\, which allows an unconditional treatment of ternary additive problem
 s even with $y$ a (large) power of $\\log x$. There are connections with r
 estriction theory and additive combinatorics.
LOCATION:MA A3 30 http://plan.epfl.ch/?lang=en&room=MA+30
STATUS:CONFIRMED
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