Abstract
For the space Lat{sub n} of all lattices in an n-dimensional p-adic linear space an analogue of the matrix beta function is constructed; this beta function can degenerate to the Tamagawa zeta function. An analogue of Berezin kernels for Lat{sub n} is proposed. Conditions for the positive-definiteness of these kernels and an explicit Plancherel's formula are obtained.
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