BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Michael J. Schlosser (Unviersity of Vienna)
DTSTART:20210607T140000Z
DTEND:20210607T150000Z
DTSTAMP:20260423T023054Z
UID:WarsawNT/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/34/
 ">On the infinite Borwein product raised to a real power</a>\nby Michael J
 . Schlosser (Unviersity of Vienna) as part of Warsaw Number Theory Seminar
 \n\nLecture held in currently online.\n\nAbstract\nWe study the $q$-series
  coefficients appearing in the expansion of $\\prod_{n\\ge 1}[(1-q^n)/(1-q
 ^{pn})]^\\delta$\, the infinite Borwein product for an arbitrary prime $p$
 \, raised to an arbitrary positive real power $\\delta$. Application of th
 e Hardy-Ramanujan-Rademacher circle method gives an asymptotic formula for
  the coefficients. For $p=3$ we give an estimate of their growth which ena
 bles us to partially confirm an earlier conjecture we made concerning an o
 bserved sign pattern of the coefficients when the exponent $\\delta$ is wi
 thin a specified range of positive real numbers. We then take a closer loo
 k at the cube of the infinite Borwein product\, for arbitrary $p$ (now a p
 ositive integer)\, and establish some vanishing and divisibility propertie
 s of the respective coefficients.\nThis is joint work with Nian Hong Zhou.
 \n
LOCATION:https://researchseminars.org/talk/WarsawNT/34/
END:VEVENT
END:VCALENDAR