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We study pseudodifferential equations and Riesz kernels attached to certainquadratic forms over p-adic fields. We attach to an elliptic quadratic form ofdimension two or four a family of distributions depending on a complexparameter, the Riesz kernels, and show that these distributions form an Abeliangroup under convolution. This result implies the existence of fundamentalsolutions for certain pseudodifferential equations like in the classical case.

Riesz Kernels and Pseudodifferential Operators Attached to Quadratic Forms Over p-adic Fields