ON THE VANISHING OF PRINCIPAL VALUE INTEG RALS

In this Note we obtain some results and stare a conjecture on the vani shing 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 integr als. They also appear as residues of poles of Igusa's local zeta funct ions. (C) Academie des Sciences/Elsevier, Paris.