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Multiplicativity of the gamma factors of Rankin–Selberg integrals for SO 2l × GL n

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Abstract

Let SO 2l be the special even orthogonal group, split or quasi–split, defined over a local non–Archimedian field. The Rankin–Selberg method for a pair of generic representations of SO 2l × GL n constructs a family of integrals, which are used to define γ and L-factors. Here we prove full multiplicative properties for the γ-factor, namely that it is multiplicative in each variable. As a corollary, the γ-factor is identical with Shahidi’s standard γ-factor.

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  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Eyal Kaplan

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  1. Eyal Kaplan
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Kaplan, E. Multiplicativity of the gamma factors of Rankin–Selberg integrals for SO 2l × GL n . manuscripta math. 142, 307–346 (2013). https://doi.org/10.1007/s00229-012-0602-x

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