On the gcd of local Rankin-Selberg integrals for even orthogonal groups

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We study the Rankin{Selberg integral for a pair of representations of SO2l × GLn, where SO2l is defined over a local non-Archimedean field and is either split or quasi-split. The integrals span a fractional ideal, and its unique generator, which contains any pole which appears in the integrals, is called the greatest common divisor (gcd) of the integrals. We describe the properties of the gcd and establish upper and lower bounds for the poles. In the tempered case we can relate it to the L-function of the representations defined by Shahidi. Results of this work may lead to a gcd definition for the L-function.

Original languageEnglish
Pages (from-to)587-636
Number of pages50
JournalCompositio Mathematica
Issue number4
StatePublished - Apr 2013
Externally publishedYes


  • L-functions
  • Rankin-Selberg integrals
  • gcd


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