Comptes rendus de l academie des sciences serie i-mathematique vol:326 issue:9 pages:1041-1046
In this Note we obtain some results and stare a conjecture on the vanishing of principal value integrals over local fields. These integrals were first introduced by Langlands. They appear as the coefficients of the asymptotic expansion of fibre integrals and of oscillating integrals. They also appear as residues of poles of Igusa's local zeta functions. (C) Academie des Sciences/Elsevier, Paris.