# Notes on the Generalized Ramanujan Conjectures

@inproceedings{Sarnak2005NotesOT, title={Notes on the Generalized Ramanujan Conjectures}, author={Peter Sarnak}, year={2005} }

1. GLn Ramanujan's original conjecture is concerned with the estimation of Fourier coe! cients of the weight 12 holomorphic cusp form " for SL(2,Z) on the upper half plane H. The conjecture may be reformulated in terms of the size of the eigen- values of the corresponding Hecke operators or equivalently in terms of the local representations which are components of the automorphic representation associated with " . This spectral reformulation of the problem of estimation of Fourier coef…

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