On the vanishing of principal value integrals |
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| Affiliation: | 1. Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA;2. Research Computing Center, Moscow State University and Moscow Center for Fundamental and Applied Mathematics, 119992 Moscow, Russia;3. Skobeltsyn Institute of Nuclear Physics, Moscow State University and Moscow Center for Fundamental and Applied Mathematics, 119992 Moscow, Russia;1. Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium;2. Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany;3. Physics Department, Florida State University, 77 Chieftan Way, Tallahassee, FL 32306, USA;4. Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, F-91191 Gif-sur-Yvette cedex, France;5. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany;1. Center for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK;2. Physics Department, FCEyN-UBA & IFIBA-CONICET, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires, Argentina |
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| Abstract: | In this Note we obtain some results and state 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. © Académie des Sciences/Elsevier, Paris |
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