The archimedean theory of the exterior square \(L\)-functions over \(\mathbb{Q}\)
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Publication:2879890
DOI10.1090/S0894-0347-2011-00719-4zbMATH Open1292.11062arXiv1109.4190OpenAlexW2964019025MaRDI QIDQ2879890
Author name not available (Why is that?)
Publication date: 5 April 2012
Published in: (Search for Journal in Brave)
Abstract: The analytic properties of automorphic L-functions have historically been obtained either through integral representations (the "Rankin-Selberg method"), or properties of the Fourier expansions of Eisenstein series (the "Langlands-Shahidi method"). We introduce a method based on pairings of automorphic distributions, that appears to be applicable to a wide variety of L-functions, including all which have integral representations. In some sense our method could be considered a completion of the Rankin-Selberg method because of its common features. We consider a particular but representative example, the exterior square L-functions on GL(n), by constructing a pairing which we compute as a product of this L-function times an explicit ratio of Gamma functions. We use this to deduce that exterior square L-functions, when multiplied by the Gamma factors predicted by Langlands, are holomorphic on C-{0,1} with at most simple poles at 0 and 1, proving a conjecture of Langlands which has not been obtained by the existing two methods.
Full work available at URL: https://arxiv.org/abs/1109.4190
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