Mathematics

Prof. Denis Benois
University of Bordeaux

We discuss extra-zeros of p-adic L-functions of motives having good reduction at p. An archetypical example is provided by the Kubota– Leopoldt L-function associated to a character χ such that χ(p) = 1 and the theorem of Ferrero and Greenberg . Other interesting examples arise from some modular forms of odd weight. In this situation, the special value of the p-adic L-function can be expressed in terms of an L -invariant defined using p-adic Hodge theory. In the both cases, trivial zeros appear in a critical point. In this talk, we are mainly interested in the non-critical case. The basic example we have in mind is provided by the Rankin–Selberg convolution of two modular forms of the same weight (joint work with S. Horte)