zbMATH — the first resource for mathematics

An \(\Omega\)-result for the coefficients of cusp forms. (English) Zbl 0254.10021

11F12 Automorphic forms, one variable
11F03 Modular and automorphic functions
Full Text: DOI EuDML
[1] Bochner, S.: Ein Satz von Landau und Ikehara. Math. Z.37, 1–9 (1933). · Zbl 0006.19604 · doi:10.1007/BF01474552
[2] Hardy, G. H.: Note on Ramanujan’s arithmetical function \(\tau\)(n). Proc. Cambridge Phil. Soc.23, 675–680 (1927). · JFM 53.0150.01 · doi:10.1017/S0305004100011178
[3] Lehmer, D. H.: Note on the distribution of Ramanujan’s tau function. Mathematics of Computation24, 741–743 (1970). · Zbl 0214.30601
[4] Niebur, D.: An average value for Ramanujan’s \(\tau\)-function. Bull. London Math. Soc.4, 23–24 (1972). · Zbl 0251.10021 · doi:10.1112/blms/4.1.23
[5] Pennington, W. B.: On the order of magnitude of Ramanujan’s arithmetical function \(\tau\)(n). Proc. Cambridge Phil. Soc.47, 668–678 (1951). · Zbl 0043.04503 · doi:10.1017/S0305004100027122
[6] Petersson, H.: Über eine Metrisierung der ganzen Modulformen. Jber. Dtsch. Mat Ver.49, 49–75 (1939). · Zbl 0021.02502
[7] Rankin, R. A.: Contributions to the theory of Ramanujan’s function \(\tau\)(n) and similar arithmetical functions. I. The zeros of the function \(\sum\limits_{n = 1}^\infty {\frac{{\tau \left( n \right)}}{{n^8 }}} \) on the line \(\operatorname{Re} s = \frac{{13}}{2}\) , Proc. Cambridge Phil. Soc.35, 351–356 (1939). · Zbl 0021.39201
[8] Rankin, R. A.: Contributions etc., II. The order of the Fourier coefficients of integral modular forms. Proc. Cambridge Phil. Soc.35, 357–372 (1939). · Zbl 0021.39202 · doi:10.1017/S0305004100021101
[9] Rankin, R. A.: The scalar product of modular forms. Proc. London Math. Soc. (3)2, 198–217 (1952). · Zbl 0049.33904 · doi:10.1112/plms/s3-2.1.198
[10] Rankin, R. A.: Ramanujan’s function \(\tau\)(n). Symposia on theoretical physics and mathematics10, 37–45 (1970). (New York: Plenum Press.)
[11] Rankin, R. A., Rushforth, J. M.: The coefficients of certain integral modular forms. Proc. Cambridge Phil. Soc.50, 305–308 (1954). · Zbl 0057.31603 · doi:10.1017/S0305004100029376
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.