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Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms

  • R. A. Rankin (a1)

Suppose that

is an integral modular form of dimensions −κ, where κ > 0, and Stufe N, which vanishes at all the rational cusps of the fundamental region, and which is absolutely convergent for Then

where a, b, c, d are integers such that ad − bc = 1.

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H. Salié , “Zur Abschätzung der Fourierkoeffizienten ganzer Modulformen”, Math. Z. 36 (1931), 263–78.

E. Hecke , “Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I”, Math. Ann. 114 (1937), 128 (Satz 5).

S. Bochner , “Ein Satz von Landau und Ikehara”, Math. Z. 37 (1933), 19.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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