Abstract
For automorphic L-functions L(s, π) and \({L( s,\pi^{\prime })}\) attached to automorphic irreducible cuspidal representations π and π′ of \({GL_{m}( \mathbb{Q}_{A})}\) and \({GL_{m^{\prime }}(\mathbb{Q}_{A}) }\), we prove the Selberg orthogonality unconditionally for m ≤ 4 and m′ ≤ 4, and under hypothesis H of Rudnik and Sarnak if m > 4 or m′ > 4, without the additional requirement that at least one of these representations be self-contragradient.
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Avdispahić, M., Smajlović, L. On the Selberg orthogonality for automorphic L-functions. Arch. Math. 94, 147–154 (2010). https://doi.org/10.1007/s00013-009-0099-z
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DOI: https://doi.org/10.1007/s00013-009-0099-z