Geodesic
$p$-adic Hecke series of imaginary quadratic fields
Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 345-371

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In this paper a $p$-adic analytic function of two variables is constructed whose values in some “common” domain coincide with the values of the family of Hecke $L$-series of an imaginary quadratic field. The functional equation for such a function is obtained. The $p$-adic Mellin integral transform is the main technique. Bibliography: 13 titles. 
@article{SM_1974_24_3_a1,
     author = {M. M. Vishik and Yu. I. Manin},
     title = {$p$-adic {Hecke} series of imaginary quadratic fields},
     journal = {Sbornik. Mathematics},
     pages = {345--371},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_3_a1/}
}
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M. M. Vishik; Yu. I. Manin. $p$-adic Hecke series of imaginary quadratic fields. Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 345-371. http://geodesic.mathdoc.fr/item/SM_1974_24_3_a1/