Generalised form of a conjecture of Jacquet and a local consequence

2006/06/21 by Dipendra Prasad, Prasad, Dipendra, Rainer Schulze‐Pillot +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #math.NT #math.RT #msc:11F70 #msc:22E50 #msc:22E55

paper · pdf · doi:10.48550/arxiv.math/0606515

20 pages. Typos corrected and some minor changes. To appear in Journal fuer die Reine und Angewandte Mathematik

arxiv created 2007/06/17 · arxiv updated 2009/12/01

Abstract

Following the work of Harris and Kudla we prove a more general form of a conjecture of Jacquet relating the non-vanishing of a certain period integral to non-vanishing of the central critical value of a certain L-function. As a consequence we deduce certain local results about the existence of GL₂(k)-invariant linear forms on irreducible, admissible representations of GL₂(\Bbb K) for \Bbb K a commutative semi-simple cubic algebra over a non-archimedean local field k in terms of certain local epsilon factors which were proved only in certain cases by the first author in his earlier work. This has been achieved by globalising a locally distinguished representation to a globally distinguished representation, a result of independent interest.

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