Zeros of Rankin-Selberg L-functions at the edge of the critical strip

Farrell Brumley, Jesse Thorner, Asif Zaman, Colin J. Bushnell, Guy Henniart

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1471-1541
Number of pages71
JournalJournal of the European Mathematical Society
Issue number5
StatePublished - 2022


  • automorphic form
  • log-free zero density estimate
  • Rankin-Selberg L-function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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