A Theorem on Analytic Strong Multiplicity One

Details A Theorem on Analytic Strong Multiplicity One A Theorem on Analytic Strong Multiplicity One

2008-12-10

arxiv.org/abs/0812.1969v1

Mathematics

Number Theory

accepted by J. Number Theory

Scientific paper

Let $K$ be an algebraic number field, and $\pi=\otimes\pi_{v}$ an irreducible, automorphic, cuspidal representation of $\GL_{m}(\mathbb{A}_{K})$ with analytic conductor $C(\pi)$. The theorem on analytic strong multiplicity one established in this note states, essentially, that there exists a positive constant $c$ depending on $\varepsilon>0, m,$ and $K$ only, such that $\pi$ can be decided completely by its local components $\pi_{v}$ with norm $N(v)

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