Geodesic
On the quadratic mean over arithmetic progressions of the Fourier coefficients of cusp forms
Izvestiya. Mathematics, Tome 22 (1984) no. 2, pp. 191-209 
M. K. Akbarov. On the quadratic mean over arithmetic progressions of the Fourier coefficients of cusp forms. Izvestiya. Mathematics, Tome 22 (1984) no. 2, pp. 191-209. http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

New theorems are obtained on the sums of the squares of the Fourier coefficients of cusp forms over arithmetic progressions with an increasing difference. Bibliography. 12 titles.

[1] Hecke E., “Über modulfunktionen und die Dirichletschen reihen mit Eulerscher produktentwicklung, I”, Math. Ann., 1937, no. 114, 1–28 | DOI | MR | Zbl

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

[3] Petersson H., “Konstruktion der sämtlichen Lösungen einer Riemannschen Funktionalgleichung durch Dirichletreihen mit Eulerscher Produktentwicklung, I”, Math. Ann., 117:1 (1939), 39–64 | DOI | MR | Zbl

[4] Rankin R. A., “I: Contribution to the theory of Ramanuijan's functions $\tau(n)$ and similar arithmetical functions. II: The order of the Fourier coefficients of integral modular forms”, Proc. Camb. Phil. Soc., 35:4 (1939), 357–372 | DOI | MR | Zbl

[5] Linnik Yu. V., “Additive problems ard eigenvalues of the modular operators”, Proc. Int. Congr. Math. Stockholm, 1962, 270–284

[6] Andrianov A. N., Fomenko O. M., “O koeffitsientakh Fure parabolicheskikh form”, DAN SSSR, 158:2 (1964), 255–257 | MR | Zbl

[7] Andrianov A. N., Fomenko O. M., “O srednikh kvadratichnykh po progressiyam koeffitsientov Fure parabolicheskikh form”, Tr. MIAN SSSR, 80, 1965, 5–15 | MR | Zbl

[8] Malyshev A. V., “O koeffitsientakh Fure modulyarnykh form”, Zap. nauchn. seminarov LOMI AN SSSR, 1, 1966, 140–163 | MR | Zbl

[9] Prakhar K., Raspredelenie prostykh chisel, M., 1967

[10] Kargapolov M. M., Merzlyakov Yu. I., Osnovy teorii grupp, M., 1972 | MR

[11] Landau E., “Über die Anzahl der Gitterpunkte in gewissen. Bereichen, II”, Gottingen Nachr. Math.-phys. Klasse, 1915, 209–243 | Zbl

[12] Landau E., Einfuhrung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale. Zweite Auflage, Leipzig, 1927