The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K})

Details The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K}) The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K})

2006-11-13

arxiv.org/abs/math/0611368v2

Mathematics

Number Theory

11 pages

Scientific paper

Let $\pi=\otimes\pi_{v}$ and $\pi^{\prime}=\otimes\pi_{v}^{\prime}$ be two irreducible, automorphic, cuspidal representations of $GL_{m}(\mathbb{A}_{K}) >.$ 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. $\pi$ and $\pi^{\prime}$ will be equal if they have finitely many same local components $\pi_{v},\pi_{v}^{\prime},$ 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 $\pi,\pi^{\prime},$ Brumley generalized this theorem by a 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 $4m+\epsilon.$

Affiliated with

Also associated with

No associations

Rating

The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K}) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K}), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Analytic Strong Multiplicity One Theorem for GL_{m}(A_{K}) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-669436