BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Agamemnon Zafeiropoulos (NTNU)
DTSTART:20220118T133000Z
DTEND:20220118T143000Z
DTSTAMP:20260423T021447Z
UID:OWNS/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/72/">Th
 e order of magnitude of Sudler products</a>\nby Agamemnon Zafeiropoulos (N
 TNU) as part of One World Numeration seminar\n\n\nAbstract\nGiven an irrat
 ional $\\alpha \\in [0\,1] \\smallsetminus \\mathbb{Q}$\, we define the co
 rresponding Sudler product by $$ P_N(\\alpha) = \\prod_{n=1}^{N}2|\\sin (\
 \pi n \\alpha)|. $$ In joint work with C. Aistleitner and N. Technau\, we 
 show that when $\\alpha = [0\;b\,b\,b…]$ is a quadratic irrational with 
 all partial quotients in its continued fraction expansion equal to some in
 teger b\, the following hold: \n\n- If $b\\leq 5$\, then $\\liminf_{N\\to 
 \\infty}P_N(\\alpha) >0$ and $\\limsup_{N\\to \\infty} P_N(\\alpha)/N < \\
 infty$. \n\n-If $b\\geq 6$\, then $\\liminf_{N\\to \\infty}P_N(\\alpha) = 
 0$ and $\\limsup_{N\\to \\infty} P_N(\\alpha)/N = \\infty$. \n\nWe also pr
 esent an analogue of the previous result for arbitrary quadratic irrationa
 ls (joint work with S. Grepstad and M. Neumueller).\n
LOCATION:https://researchseminars.org/talk/OWNS/72/
END:VEVENT
END:VCALENDAR