Airy integrals are very classical but in recent years they have been
generalized to higher dimensions and these generalizations have proved to be
very useful in studying the topology of the moduli spaces of curves. We study a
natural generalization of these integrals when the ground field is a
non-archimedean local field such as the field of p-adic numbers. We prove that
the p-adic Airy integrals are locally constant functions of moderate growth and
present evidence that the Airy integrals associated to compact p-adic Lie
groups also have these properties.Comment: Minor change