Posted in

Speaker:

Denis Benois
Affiliation:

U. Bordeaux / MPIM
Date:

Tue, 2017-06-13 14:00 - 15:00
Location:

MPIM Lecture Hall
Parent event:

Seminar on Algebra, Geometry and Physics One says that a $p$-adic $L$-function has an extra zero if the $p$-adic

interpolation property forces it to vanish at some integer point.

In the case of elliptic modular forms, this phenomenon was first

studied by Mazur, Tate and Teitelbaum in 1986. They conjectured that

in the presence of a trivial zero the special value of the $p$-adic $L$-function

at the central point is related to the special value of the corresponding complex

$L$-function via a new invariant defined in terms of the $p$-adic Hodge theory.

In this talk we discuss a quite general conjecture describing special

values of $p$-adic $L$-functions at extra-zeros focusing on the

non-critical point case and present some new results in this direction.

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