Computing the values of Ramanujan's tau-function

Robin de Jong

We give an overview of a result due to B. Edixhoven, J.M. Couveignes and the speaker that Ramanujan's tau for prime numbers p can be computed in time polynomial in log p. We show that the problem is really an instance of 'computing Galois representations associated to modular forms'. We also discuss recent generalisations of the result to modular forms of 'level one but arbitrary weight' and to modular forms of 'arbitrary level and weight', the latter being due to Peter Bruin.

Applications and a motivation of the problem will be sketched as well.

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