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Paul Nelson (Aarhus University)

Title: Shears and moments of L-functions in higher rank

Abstract: We present an integral representation for moments of L-functions on GL(n), ordered by analytic conductor, involving L^2-norms of "shears" (pure unipotent translates) of fixed automorphic forms on larger groups. Quantitative equidistribution of such shears would yield an effective asymptotic formula. These observations apply in particular to the (4n)th moment, for an effective asymptotic formula would yield a subconvex bound, going beyond the case of "uniform parameter growth" treated by previous approaches. Joint work with Subhajit Jana.