Summation formulae for quadrics

• Jayce R. Getz ^[1]
  1. [1] Duke University

     Duke University

     Township of Durham, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved.

    The key novelty in the formula is that all “boundary terms” are given either by constants or sums over smaller quadrics related to the original quadric. We also discuss the link with the classical problem of estimating the number of solutions of a quadratic form in an even number of variables. To prove the summation formula we compute (the Arthur truncated) theta lift of the trivial representation of SL2(AF ). As previously observed by Ginzburg, Rallis, and Soudry, this is an analogue for orthogonal groups on vector spaces of even dimension of the global Schrödinger representation of the metaplectic group.

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