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Fourier coefficients of cusp forms. (English) Zbl 0616.10020

This is a very good survey article whose object is to trace the influence of the theory of modular forms after the ideas in L. J. Mordell’s famous paper ”On Mr. Ramanujan’s empirical expansions of modular functions”, Proc. Camb. Philos. Soc. 19, 117-124 (1917), mainly in a line or around Ramanujan, Mordell, Hecke, Petersson, Atkin, Lehner and others.
The divisibility properties of cusp form coefficients, modular forms of many variables and non-holomorphic forms are left untouched because they are subjects to be written in separate articles, but it is strongly hoped that these topics should be surveyed in the future.
Reviewer: K.Katayama

MSC:

11F11 Holomorphic modular forms of integral weight
11-02 Research exposition (monographs, survey articles) pertaining to number theory
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