Geodesic
Non-Archimedean integration and Jacquet--Langlands $p$-adic $L$-functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 1, pp. 5-57

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In 1964 Kubota and Leopoldt constructed a $p$-adic analogue of the Riemann zeta-function. Since then the class of $L$-functions with $p$-adic variants has continually been enlarged. At the beginning of the article we survey work in this direction, using the technique of the $p$-adic Mellin transform. Then we show how to apply it to the construction of non-Archimedean measures and integrals corresponding to parabolic forms relative to the Hilbert groups. The exposition is in the adele language of Jacquet and Langlands. We construct $p$-adic $L$-functions associated with representations of $GL(2)$ over completely real fields, of discrete type at infinity. 
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     title = {Non-Archimedean integration and {Jacquet--Langlands} $p$-adic $L$-functions},
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}
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Yu. I. Manin. Non-Archimedean integration and Jacquet--Langlands $p$-adic $L$-functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 1, pp. 5-57. http://geodesic.mathdoc.fr/item/RM_1976_31_1_a1/