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SUMMARY:Paul Pollack (University of Georgia)
DTSTART:20220526T180000Z
DTEND:20220526T182500Z
DTSTAMP:20260423T011320Z
UID:CANT2022/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/39/
 ">Weak uniform distribution of certain arithmetic functions</a>\nby Paul P
 ollack (University of Georgia) as part of Combinatorial and additive numbe
 r theory (CANT 2022)\n\n\nAbstract\nFor any fixed integer $q$\, it is a cl
 assical result (implicit in work of Landau\, and perhaps known earlier) th
 at Euler's function $\\phi(n)$ is a multiple of $q$ asymptotically 100\\% 
 of the time. Thus\, $\\phi(n)$ is very far from being uniformly distribute
 d mod $q$ in the usual sense (unless $q=1$ !). On the other hand\, Narkiew
 icz has proved that $\\phi(n)$ is weakly uniformly distributed mod $q$ whe
 never $q$ is coprime to 6\; “weakly” means that every coprime residue 
 class mod $q$ gets its fair share of values $\\phi(n)$\, from among the $n
 $ with $\\phi(n)$ coprime to $q$. In fact\, Narkiewicz proves this not jus
 t for $\\phi$ but for a wide class of “polynomially-defined” multiplic
 ative functions. In this talk\, we will consider these weak uniform distri
 bution problems with an eye towards obtaining wide ranges of uniformity in
  the modulus $q$. \n\nThis is joint work with Noah Lebowitz-Lockard and Ak
 ash Singha Roy.\n
LOCATION:https://researchseminars.org/talk/CANT2022/39/
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