Geodesic
Beta functions of Bruhat–Tits buildings and deformation of $l^2$
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1775-1805 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the space $\operatorname{Lat}_n$ 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 $\operatorname{Lat}_n$ is proposed. Conditions for the positive-definiteness of these kernels and an explicit Plancherel's formula are obtained. 
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     title = {Beta functions of {Bruhat{\textendash}Tits} buildings and deformation of $l^2$},
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Yu. A. Neretin. Beta functions of Bruhat–Tits buildings and deformation of $l^2$. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1775-1805. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a1/

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