局部域上的Airy函数
Airy functions over local fields
摘要：
Airy积分是非常经典的，但近年来，他们已被推广到高维，这些推广已被证明是非常有用的研究拓扑的模空间的曲线。我们研究这些积分的自然推广时，地面领域是一个非阿基米德的局部领域，如领域的p-adic数。我们证明了p-adic艾里积分是局部常数函数的适度增长，并提出证据表明，与紧凑的p-adic李群的艾里积分也有这些属性。
英文摘要：
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.
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