### Sur le rang de J_0(q), by Emmanuel Kowalski and Philippe Michel

In this paper, we prove an unconditionnal bound for the analytic rank (i.e
the order of vanishing at the critical point of the $L$ function) of the new
part $J^n_0(q)$, of the jacobian of the modular curve $X_0(q)$. Our main
resultis the following upper bound: for $q$ prime, one has
$$rank_a(J_0^n(q))\ll \dim J_0^n(q)$$ where the implied constant is
absolute. All previously known non trivials bounds of $rank_a(J_0^n(q))$
assumed the generalized Riemann hypothesis; here, our proof is
unconditionnal, and is based firstly on the construction by Perelli and
Pomykala of a new test function in the context of Riemann-Weil explicit
formulas, and secondly on a density theorem for the zeros of $L$ functions
attached to new forms.

Emmanuel Kowalski <ekowalsk@math.rutgers.edu>
Philippe Michel <michel@math.u-psud.fr>