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Journal of the Ramanujan Mathematical Society

Volume 39, Issue 1, March 2024  pp. 55–63.

On equidistribution of Gauss sums of cuspidal representations of GL{d}(𝔽{q}) and PGL{d}(𝔽{q})

Authors:  Sameer Kulkarni and C. S. Rajan
Author institution: Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India.

Summary:  We investigate the distribution of the angles of the normalised Gauss sums attached to the cuspidal representations of general linear groups over finite fields. In particular we show that they happen to be equidistributed w.r.t. the Haar measure. However, for representations of PGL{2}(𝔽{q}), they are equal identically to 1 and −1 when q is odd, and are 1 for q even.

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