Let π (respectively π0) be a unitary cuspidal automorphic representation of GLm (respectively GLm0 ) over Q. We prove log-free zero density estimates for Rankin-Selberg Lfunctions of the form L(s;π × π0), where π varies in a given family and π0 is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maaß forms, the rarity of Landau-Siegel zeros of Rankin-Selberg L-functions, the Chebotarev density theorem, and torsion in class groups of number fields.
- automorphic form
- log-free zero density estimate
- Rankin-Selberg L-function
ASJC Scopus subject areas
- Applied Mathematics