We shall first briefly recall some results on distribution of Hecke eigenvalues of elliptic cusp forms. Then we describe our recent results on joint distribution of these eigenvalues for CM and non-CM eigenforms. Further, we relate these distributions to simultaneous sign change of the eigenvalues. As a consequence of our result, we derive an equivalent formulation of Lehmer conjecture about non-vanishing of the Ramanujan tau-function in terms of sign change of the tau function. This talk is based on a recent joint work with S. Gun and V. Kumar Murty.

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