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arXiv · 2208.01783

Averages of quadratic twists of long Dirichlet polynomials

Brian Conrey·Brad Rodgers
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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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Brian Conrey, Brad Rodgers. 2022-08-02. Averages of quadratic twists of long Dirichlet polynomials. https://arxiv.org/abs/2208.01783

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