Refinement of strong multiplicity one for automorphic representations of 𝐺𝐿(𝑛)

Rajan, C.

doi:10.1090/S0002-9939-99-05616-6

Refinement of strong multiplicity one for automorphic representations of $GL(n)$
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Proc. Amer. Math. Soc. 128 (2000), 691-700 Request permission

Abstract:

We state a qualitative form of strong multiplicity one for $GL_1$. We derive refinements of strong multiplicity one for automorphic representations arising from Eisenstein series associated to a Borel subgroup on $GL(n)$, and for the cuspidal representations on $GL(n)$ induced from idele class characters of cyclic extensions of prime degree. These results are in accordance with a conjecture of D. Ramakrishnan. We also show that Ramakrishnan’s conjecture follows from a weak form of Ramanujan’s conjecture. We state a conjecture concerning the structural aspects of refinements of strong multiplicity one for a pair of general automorphic representations.

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