Weighted vertical equidistribution of Satake parameters for GSp(4)

Abstract: The automorphic representations of an algebraic group G factor as a restricted tensor product of local representations. In turn, these local representations are parametrised by their Satake parameters. One can ask what properties the Satake parameters that do arise from automorphic representations of G have to satisfy. For instance, in the verical distribution problem, one fixes a prime p and asks for the distribution of the Satake parameters at p of automorphic representations of G varying in some families amenable to the theory of (relative) trace formulae. In this talk, I discuss the case of Maass forms on G=GSp(4). When counted with a suitable weight coming from the Kuznetsov formula, the Satake parameters equidistribute with respect to the Sato-Tate measure. This is consistent with the generalised Ramanujan conjecture, expected to hold in this situation.

number theory

Audience: researchers in the topic

London number theory seminar

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