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SUMMARY:Marco Streng (Universiteit Leiden)
DTSTART:20210517T111500Z
DTEND:20210517T121500Z
DTSTAMP:20260423T023053Z
UID:WarsawNT/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/31/
 ">Obtaining modular units via a recurrence relation</a>\nby Marco Streng (
 Universiteit Leiden) as part of Warsaw Number Theory Seminar\n\nLecture he
 ld in currently online.\n\nAbstract\nThe modular curve $Y^1(N)$ parametris
 es pairs $(E\,P)$\, where $E$ is an elliptic curve and $P$ is a point of o
 rder $N$ on $E$. One tool for studying this curve is the group of modular 
 units on it\, that is\, the group of algebraic functions with no poles or 
 zeroes.\n\nWe first review how a recurrence relation (related to elliptic 
 divisibility sequences) gives rise to defining equations for the curves $Y
 ^1(N)$. We then show that the same recurrence relation also gives explicit
  algebraic formulae for a basis of the group of units on $Y^1(N)$.\n\nThis
  proves a conjecture of Maarten Derickx and Mark van Hoeij.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/31/
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