Geodesic
Convolutions of Hecke series and their values at lattice points
Sbornik. Mathematics, Tome 33 (1977) no. 4, pp. 539-571 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An algebraicity theorem is proved for the values of convolutions of Dirichlet series connected with modular forms of various weights at lattice points of the critical strip, $p$-adic estimates of these values are obtained. Bibliography: 24 titles. 
@article{SM_1977_33_4_a5,
     author = {Yu. I. Manin and A. A. Panchishkin},
     title = {Convolutions of {Hecke} series and their values at lattice points},
     journal = {Sbornik. Mathematics},
     pages = {539--571},
     year = {1977},
     volume = {33},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_4_a5/}
}
TY  - JOUR
AU  - Yu. I. Manin
AU  - A. A. Panchishkin
TI  - Convolutions of Hecke series and their values at lattice points
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 539
EP  - 571
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1977_33_4_a5/
LA  - en
ID  - SM_1977_33_4_a5
ER  - 
%0 Journal Article
%A Yu. I. Manin
%A A. A. Panchishkin
%T Convolutions of Hecke series and their values at lattice points
%J Sbornik. Mathematics
%D 1977
%P 539-571
%V 33
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1977_33_4_a5/
%G en
%F SM_1977_33_4_a5
Yu. I. Manin; A. A. Panchishkin. Convolutions of Hecke series and their values at lattice points. Sbornik. Mathematics, Tome 33 (1977) no. 4, pp. 539-571. http://geodesic.mathdoc.fr/item/SM_1977_33_4_a5/

[1] M. M. Vishik, “Nearkhimedovy mery, svyazannye s ryadami Dirikhle”, Matem. sb., 99(141) (1976), 248–260 | Zbl

[2] M. M. Vishik, Yu. I. Manin, “$\mathfrak{p}$-adicheskie ryady Gekke mnimykh kvadratichnykh polei”, Matem. sb., 95 (137) (1974), 357–383 | MR | Zbl

[3] R. K. Ganning, “Lektsii o modulyarnykh formakh”, Matematika, 8:6 (1964), 3–68

[4] P. Delin, “Modulyarnye formy i $l$-adicheskie predstavleniya”, Zh.-P. Serr, Abelevy 1-adicheskie predstavleniya i ellipticheskie krivye, Prilozhenie, izd-vo «Mir», Moskva, 1973

[5] P. Delin, “Gipoteza Veilya”, Uspekhi matem. nauk, XXX:5 (185) (1975), 159–190 | MR

[6] K. Doi, H. Naganuma, “On the functional equation of certain Dirichlet series”, Inv. Math., 9:1 (1969), 1–14 | DOI | MR | Zbl

[7] E. Hecke, “Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionaltheorie und Arithmetik”, Mathematische Werke, Göttingen, 1959, 461–481 | MR

[8] E. Hecke, “Analytische Funktionen und Algebraische Zahlen, II”, Mathematische Werke, Göttingen, 1959, 381–398

[9] E. Hecke, “Darstellung von Klassenzahlen als Perioden von Integral. 3: Gattung”, Mathematische Werke, Göttingen, 1959, 381–398 | MR

[10] H. Jacquet, Automorphic functions on $\mathrm{GL(2)}$, Part II, Lecture Notes in Math., 278, Springer-Verlag, Berlin–Heidelberg–New York, 1972 | MR | Zbl

[11] T. Kubota, H. W. Leopoldt, “Eine $p$-adische Theorie der Zeta Werte”, J. angew. Math., 214–215 (1964), 328–339 | MR | Zbl

[12] W.-C. W. Li, “Newforms and functional equations”, Math. Ann., 212:4 (1975), 285–315 | DOI | MR | Zbl

[13] S. Lichtenbaum, “On the values of zeta- and $L$-series”, Ann. Math., 96:2 (1972), 338–360 | DOI | MR | Zbl

[14] Yu. I. Manin, “Periody parabolicheskikh form i $p$-adicheskie ryady Gekke”, Matem. sb., 92 (134) (1973), 378–401 | MR | Zbl

[15] Yu. I. Manin, “Znacheniya $p$-adicheskikh ryadov Gekke v tselykh tochkakh kriticheskoi polosy”, Matem. sb., 93 (135) (1974), 621–626 | MR | Zbl

[16] Yu. I. Manin, “Nearkhimedovo integrirovanie i $p$-adicheskie $L$-funktsii Zhake-Lenglendsa”, Uspekhi matem. nauk, XXXI:1 (185) (1976), 5–53 | MR

[17] B. Mazur, H. P. F. Swinnerton-Dyer, “Arithmetic of Weil curves”, Inv. Math., 25:1 (1974), 1–61 | DOI | MR | Zbl

[18] A. P. Ogg, “On a convolution of $L$-series”, Inv. Math., 7:4 (1969), 297–312 | DOI | MR | Zbl

[19] R. A. Rankin, “The scalar product of modular forms”, Proc. London Math. Soc., 2:6 (1962), 198–217 | MR

[20] R. A. Rankin, “Contribution to the theory of Ramanujans function $\tau(n)$ and similar arithmetical functions. I; II”, Proc. Camb. Phil. Soc., 35 (1939), 351–356 ; 357–372 | DOI | MR | Zbl | Zbl

[21] A. Selberg, “Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist”, Arch. Math. Naturwis., 43 (1940), 47–50 | MR

[22] C. L. Siegel, Lectures on advanced analytic number theory, Tata Institut, Bombay, 1965 | MR | Zbl

[23] G. Shimura, Vvedenie v arifmeticheskuyu teoriyu avtomorfnykh funktsii, izd-vo «Mir», Moskva, 1973 | MR

[24] D. Zagier, “Modular forms associated to real quadratic fields”, Inv. Math., 30:1 (1975), 1–46 | DOI | MR | Zbl