Article ID Journal Published Year Pages File Type
4595288 Journal of Number Theory 2008 11 Pages PDF
Abstract

Let π=⊗πv and be two irreducible, automorphic, cuspidal representations of GLm(AK). Using the logarithmic zero-free region of Rankin–Selberg L-function, Moreno established the analytic strong multiplicity one theorem if at least one of them is self-contragredient, i.e. π and π′ will be equal if they have finitely many equivalent local components , for which the norm of places are bounded polynomially by the analytic conductor of these cuspidal representations. Without the assumption of the self-contragredient for π,π′, Brumley generalized this theorem by a different method, which can be seen as an invariant of Rankin–Selberg method. In this paper, influenced by Landau's smooth method of Perron formula, we improved the degree of Brumley's polynomial bound to be 4m+ε.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory