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Archiv der Mathematik

, Volume 94, Issue 2, pp 147–154 | Cite as

On the Selberg orthogonality for automorphic L-functions

  • Muharem Avdispahić
  • Lejla Smajlović
Article

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.

Mathematics Subject Classification (2000)

11F03 11M26 11F70 

Keywords

Automorphic L-functions Rankin-Selberg L-function Selberg’s orthogonality 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SarajevoSarajevoBosnia and Herzegovina

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