Geodesic
Periods of parabolic forms and $p$-adic Hecke series
Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 371-393 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author proves an algebraicity theorem for the periods of parabolic forms of any weight for the full modular group, gives explicit formulas for the coefficients of the forms, and constructs $p$-adic analogs of their Mellin transforms in the manner of Iwasawa and Mazur. Bibliography: 13 titles. 
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     author = {Yu. I. Manin},
     title = {Periods of parabolic forms and $p$-adic {Hecke} series},
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Yu. I. Manin. Periods of parabolic forms and $p$-adic Hecke series. Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 371-393. http://geodesic.mathdoc.fr/item/SM_1973_21_3_a1/

[1] K. Iwasawa, Lectures on $p$-adic $L$-functions, Ann. Math. Studies, 74, Princeton Univ. Press, 1972 | MR | Zbl

[2] H. Jacquet, R. P. Langlands, Automorphic functions on $CL(2)$, Lecture notes in math., 114, Springer-Verlag, Berlin, 1970 | MR | Zbl

[3] Yu. I. Manin, “Krugovye polya i modulyarnye krivye”, Uspekhi matem. nauk, XXVI:6 (162) (1971), 7–71 | MR

[4] Yu. I. Manin, “Parabolicheskie tochki i dzeta-funktsii modulyarnykh krivykh”, Izv. AN SSSR, seriya matem., 36 (1972), 19–66 | MR | Zbl

[5] Yu. I. Manin, “Explicit formulas for the eigenvaluas of Heoke operators”, Acta Arithmetica, XXIV (1973), 239–249 | MR

[6] B. Mazur, H. P. F. Swinnerton-Dyer, On the $p$-adic $L$-series of an elliptic curve, preprint | MR

[7] S. Ramanujan, “On certain arithmetical functions”, Trans. Cambridge Phil. Soc., 22 (1916), 159–184

[8] Zh. P. Serr, Kurs arifmetiki, izd-vo «Mir», Moskva, 1972 | MR

[9] Zh. P. Serr, “Interpretatsiya sravnenii, svyazannykh s funktsiei Ramanudzhana”, Matematika, 13:4 (1969), 3–15 | MR

[10] Zh. P. Serr, “Sravneniya i modulyarnye formy”, Uspekhi matem. nauk, XXVIII:2 (170) (1973), 183–196 | MR

[11] J. P. Serre, “Formes modulaires et fonctions zêta $p$-adiques”, Summer School on Modular functions, Antwerp., 1972 | MR

[12] H. P. F. Swinnerton-Dyer, “On $l$-adic representations and congruences for coefficients of modular forms”, Summer School on Modular functions, Antwerp., 1972 | MR

[13] G. Shimura, “Ob integralakh, svyazannykh s avtomorfnymi formami”, Matematika, 9:3 (1965), 130–150