Functional Equations of $L$-Functions for Symmetric Products of the Kloosterman Sheaf

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dc.creatorFu, Lei
dc.creatorWan, Daqing
dc.date2008-12-30
dc.date.accessioned2026-07-07T12:23:07Z
dc.date.available2026-07-07T12:23:07Z
dc.descriptionWe determine the (arithmetic) local monodromy at 0 and at $\infty$ of the Kloosterman sheaf using local Fourier transformations and Laumon's stationary phase principle. We then calculate $ε$-factors for symmetric products of the Kloosterman sheaf. Using Laumon's product formula, we get functional equations of $L$-functions for these symmetric products, and prove a conjecture of Evans on signs of constants of functional equations.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0812.4994
dc.identifierhttp://arxiv.org/abs/0812.4994
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213878
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11L05, 14G15
dc.titleFunctional Equations of $L$-Functions for Symmetric Products of the Kloosterman Sheaf
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