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SUMMARY:Felix Baril Boudreau (U. of Lethbridge)
DTSTART:20230411T193000Z
DTEND:20230411T203000Z
DTSTAMP:20260405T182230Z
UID:ANTULaval/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTULaval/21
 /">L-Functions of Elliptic Curves in Positive Characteristic (Part II : St
 udying L-Functions of Elliptic Curves over Function Fields via their Reduc
 tion Modulo Integers)</a>\nby Felix Baril Boudreau (U. of Lethbridge) as p
 art of Algebra and Number Theory Seminars at Université Laval\n\n\nAbstra
 ct\nElliptic curves are a central object of study in number theory. In thi
 s talk\, we focus on those defined over function fields and with nonconsta
 nt j-invariant. The L-function of such an elliptic curve E/K is polynomial
  with integer coefficients.\n\nInspired by Schoof's algorithm\, we study t
 he reduction modulo integers of the L-function. More precisely\, when E(K)
  has nontrivial N-torsion\, we give formulas for the reductions modulo 2 a
 nd N for any quadratic twist of E/K. This generalizes a formula obtained b
 y Chris Hall for E/K. We give examples where we can compute the global roo
 t number of the quadratic twists\, the order of vanishing of the L-functio
 n at a special value and even the whole L-function from these reductions. 
 However\, the group E(K) is finitely generated and in particular has finit
 e torsion. Time permiting\, we discuss some of our work in progress in thi
 s situation. More precisely\, given a prime ell different from char(K)\, w
 e provide\, in absence of nontrivial ell-torsion and in a quite general co
 ntext\, expressions for the reduction modulo ell of the L-function.\n\nThe
  talk will be given in English\n
LOCATION:https://researchseminars.org/talk/ANTULaval/21/
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