Geodesic
Non-Archimedean Rankin convolutions of unbounded growth
Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 151-161

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Non-Archimedean Rankin convolutions are constructed in the supersingular case. The construction is based on a refined technique of $h$-admissible measures, for which the non-Archimedean Mellin transform gives analytic functions of unbounded growth. 
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     author = {My Vinh Quang},
     title = {Non-Archimedean {Rankin} convolutions of unbounded growth},
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My Vinh Quang. Non-Archimedean Rankin convolutions of unbounded growth. Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 151-161. http://geodesic.mathdoc.fr/item/SM_1992_72_1_a8/