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Pairings of automorphic distributions

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Abstract

We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties. The pairing gives meaning to an integral of products of automorphic distributions on these varieties. This generalizes classical integral representations or “Rankin–Selberg integrals” of L-functions, and gives new constructions and analytic continuations of automorphic L-functions.

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Authors and Affiliations

  1. Department of Mathematics, Hill Center, Busch Campus Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ, 08854-8019, USA

    Stephen D. Miller

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Wilfried Schmid

Authors
  1. Stephen D. Miller
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  2. Wilfried Schmid
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Correspondence to Stephen D. Miller.

Additional information

Partially supported by NSF Grants DMS-0500922 and DMS-0601009, and DARPA Grant HR0011-04-1-0031.

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Miller, S.D., Schmid, W. Pairings of automorphic distributions. Math. Ann. 353, 581–597 (2012). https://doi.org/10.1007/s00208-011-0685-9

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  • DOI: https://doi.org/10.1007/s00208-011-0685-9

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