Article ID Journal Published Year Pages File Type
6425928 Advances in Mathematics 2012 25 Pages PDF
Abstract

Many important analytic statements about automorphic forms, such as the analytic continuation of certain L-functions, rely on the well-known rapid decay of K-finite cusp forms on Siegel sets. We extend this here to prove a more general decay statement along sets much larger than Siegel sets, and furthermore state and prove the decay for smooth but not necessarily K-finite cusp forms. We also state a general theorem about the convergence of Rankin-Selberg integrals involving unipotent periods, closing a gap in the literature on L-functions. These properties serve as the analytic basis (Miller and Schmid, 2009 [15]) of a new method to establish holomorphic continuations of Langlands L-functions, in particular the exterior square L-functions (Miller and Schmid, 2009 [16]) on GL(n).

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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