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Averages of quadratic twists of long Dirichlet polynomials

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arxiv 2208.01783 v2 pith:FUAQM5WW submitted 2022-08-02 math.NT

Brian Conrey , Brad Rodgers This is my paper · ORCID
classification math.NT
keywords averagesrecipedirichletlongpolynomialsquadratictermsable
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abstract

We investigate averages of long Dirichlet polynomials twisted by Kronecker symbols and we compare our result with the recipe of [CFKRS]. We are able to compute these averages in the case that the length of the polynomial is a power less than 2 of the basic scaling parameter on the assumption of the Lindel\"of Hypothesis for $L$-functions of quadratic characters, and we show that the answer is consistent with this recipe. This corresponds, in terms of the recipe, to verifying 0- and 1-swap terms.

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  1. Multiple Dirichlet series predictions for moments of $L$-functions: unitary, symplectic and orthogonal examples

    math.NT 2025-01 conditional novelty 6.0 of 10

    Multiple Dirichlet series heuristics reproduce, and for elliptic curve twists correct, the standard moment predictions for four families of L-functions, with each recipe term matched to a residue.

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