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SUMMARY:Ioannis Tsokanos (The University of Manchester)
DTSTART:20221031T140000Z
DTEND:20221031T150000Z
DTSTAMP:20260423T053137Z
UID:GANT/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GANT/15/">De
 nsity of oscillating sequences in the real line</a>\nby Ioannis Tsokanos (
 The University of Manchester) as part of Greek Algebra & Number Theory Sem
 inar\n\n\nAbstract\nIn this talk\, we study the density properties in the 
 real line of oscillating sequences of the form $( g(k) \\cdot F(ka) )_{k \
 \in \\mathbb{N}}$\,  where $g$ is a positive increasing function and $F$ a
  real continuous $1$-periodic function. This extends work by Berend\, Bosh
 ernitzan and Kolesnik who established differential properties on the funct
 ion $F$ ensuring that the oscillating sequence is dense modulo $1$. More p
 recisely\, when F has finitely many roots in $[0\,1)$\, we provide necessa
 ry and sufficient conditions for the oscillating sequence under considerat
 ion to be dense in $\\mathbb{R}$. All the related results are stated in te
 rms of the Diophantine properties of $a$\, with the help of the theory of 
 continued fractions.\n
LOCATION:https://researchseminars.org/talk/GANT/15/
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