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Theta dichotomy for the genuine unramified principal series of \({\widetilde{Sp}_2(F)}\)

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Abstract

Let F be a p-adic field with odd residual characteristic. This work is the continuation of a previous paper that contains some detailed computations of the doubling integral for irreducible constituents \({(\pi, \mathcal{V}_{\pi})}\) of the genuine unramified principal series of \({\widetilde{Sp}_2(F)}\) using various “good test data”. This paper aims to interpret those results in terms of the non-vanishing of local theta lifts. Assuming a technical condition on order of a particular pole for the family of doubling integrals for \({(\pi, \mathcal{V}_{\pi})}\) , we aim to determine the so-called “dichotomy sign” of \({(\pi, \mathcal{V}_{\pi})}\) .

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  1. Mathematics Department, Boston College, 254 Carney Hall, 140 Commonwealth Avenue, Chestnut Hill, MA, 02467, USA

    Christian A. Zorn

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Zorn, C.A. Theta dichotomy for the genuine unramified principal series of \({\widetilde{Sp}_2(F)}\) . manuscripta math. 137, 159–194 (2012). https://doi.org/10.1007/s00229-011-0462-9

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