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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213878We 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.23 pagesNumber TheoryAlgebraic Geometry11L05, 14G15Functional Equations of $L$-Functions for Symmetric Products of the Kloosterman Sheaftext