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SUMMARY:Robert Slob (Ulm University)
DTSTART:20210510T111500Z
DTEND:20210510T121500Z
DTSTAMP:20260423T041612Z
UID:WarsawNT/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/30/
 ">Primitive divisors of sequences associated to elliptic curves over funct
 ion fields</a>\nby Robert Slob (Ulm University) as part of Warsaw Number T
 heory Seminar\n\nLecture held in currently online.\n\nAbstract\nIn the fir
 st part of the talk\, we give a gentle introduction into the subject of di
 visibility sequences over the rational numbers and discuss the notion of a
  primitive divisor/Zsigmondy bound. We then explain how these notions can 
 be extended to number fields and function fields\, and how to obtain a div
 isibility sequence from a non-torsion point on an elliptic curve over any 
 of these fields. There will also be plenty of nice examples.\n\nIn the sec
 ond part of the talk\, we discuss the typical methods that are used to pro
 ve the existence of a Zsigmondy bound for a divisibility sequence obtained
  from a non-torsion point on an elliptic curve $E$ over a number or functi
 on field $K$. Let $P$ be this non-torsion point in $E(K)$\, and suppose Q 
 is a torsion point in $E(K)$. We can also associate a sequence of divisors
  $\\{D_{nP+Q}\\}$ on $K$ to the sequence of points $\\{nP+Q\\}$. In my pre
 print\, we proved the existence of a Zsigmondy bound for this sequence $\\
 {D_{nP+Q}\\}$ for $K$ a function field (under some minor conditions)\, ext
 ending the analogous result of Verzobio over number fields. I will provide
  the crucial ideas to apply the existing methods of the case $\\{nP\\}$ to
  my case $\\{nP+Q\\}$. Additionally\, I will highlight the differences wit
 h the number field case.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/30/
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