Recovering modular forms and representations from tensor and symmetric powers

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We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if the characters of some tensor or symmetric powers of two absolutely irreducible $l$-adic representation with the algebraic envelope of the image being connected, agree at the Frobenius elements corresponding to a set of places of positive upper density, then the representations are twists of each other by a finite order character.
18 pages; this is a revised version of a paper submitted to the old Number Theory archive as ANT-0357

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Number Theory, Primary 11F80; Secondary 11R45

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http://salesiana.dossiersoluciones.com/handle/123456789/72917

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410387
 http://arxiv.org/abs/math/0410387

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arXiv