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

Author(s): C. S. Rajan
Journal: Proc. Amer. Math. Soc. 128 (2000), 691-700.
MSC (1991): Primary 11F70; Secondary 11F12, 22E55
Posted: October 20, 1999
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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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Additional Information:

C. S. Rajan
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400 005, India
Email: rajan@math.tifr.res.in

DOI: 10.1090/S0002-9939-99-05616-6
PII: S 0002-9939(99)05616-6
Received by editor(s): April 28, 1998
Posted: October 20, 1999
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 1999, American Mathematical Society

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