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SUMMARY:Drinfeld type automorphic forms and special values of L-functions
over function fields
DTSTART;VALUE=DATE-TIME:20140211T143000Z
DTEND;VALUE=DATE-TIME:20140211T150000Z
DTSTAMP;VALUE=DATE-TIME:20190719T212223Z
UID:indico-event-386@indico.math.cnrs.fr
DESCRIPTION:By a function field K\, we mean a field extension over a finit
e field with transcendence degree one. In the function field world\, by th
e work of Deligne\, Drinfeld\, Jacquet-Langlands\, Weil\, and Zarhin\, the
"Drinfeld modular parametrization" always exists for every "non-isotrivia
l" elliptic curve E over K. Suppose E has split multiplicative reduction a
t a place ∞. Then there exists a unique "Drinfeld type" (with respect to
∞) automorphic cusp form fE such that its L-function coincides with the
Hasse-Weil L-function of E over K. These forms can be viewed as analogue
of classical weight 2 modular forms. In this talk\, we will start with bas
ic properties of Drinfeld type automorphic forms\, and use them as tools t
o obtain explicit formulas for special values of the L-functions coming fr
om non-isotrivial elliptic curves.\n\nhttps://indico.math.cnrs.fr/event/38
6/
LOCATION:IHES Amphitéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/386/
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