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UID:news1740@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20241010T184436
DTSTART;TZID=Europe/Zurich:20241031T141500
SUMMARY:Number Theory Seminar: Alina Ostafe (University of New South Wales)
DESCRIPTION:Title: On the frequency of primes preserving dynamical irreduci
 bility of polynomials\\r\\nAbstract: In this talk we address an open quest
 ion in arithmetic dynamics regarding the frequency of primes modulo which 
 all the iterates of an integer polynomial remain irreducible. More precise
 ly\, for a class of integer polynomials $f$\, which in particular includes
  all quadratic polynomials\, we show that\, under some natural conditions\
 , the set of primes $p$ such that all iterates of $f$ are irreducible modu
 lo $p$ is of relative density zero. Our results rely on a combination of a
 nalytic (Selberg's sieve) and Diophantine (finiteness of solutions to cert
 ain hyperelliptic equations) tools\, which we will briefly describe. Joint
  wok with Laszlo Mérai and Igor Shparlinski (2021\, 2024).\\r\\nSpiegelga
 sse 5\, Seminarraum 05.002
X-ALT-DESC:<p>Title: On the frequency of primes preserving dynamical irredu
 cibility of polynomials</p>\n<p>Abstract: In this talk we address an open 
 question in arithmetic dynamics regarding the frequency of primes modulo w
 hich all the iterates of an integer polynomial remain irreducible. More pr
 ecisely\, for a class of integer polynomials $f$\, which in particular inc
 ludes all quadratic polynomials\, we show that\, under some natural condit
 ions\, the set of primes $p$ such that all iterates of $f$ are irreducible
  modulo $p$ is of relative density zero. Our results rely on a combination
  of analytic (Selberg's sieve) and Diophantine (finiteness of solutions to
  certain hyperelliptic equations) tools\, which we will briefly describe. 
 Joint wok with Laszlo Mérai and Igor Shparlinski (2021\, 2024).</p>\n<p>S
 piegelgasse 5\, Seminarraum 05.002</p>
DTEND;TZID=Europe/Zurich:20241031T151500
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