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Creators/Authors contains: "Turnage-Butterbaugh, Caroline L"

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  1. ; (, International Mathematics Research Notices)
    Consider the family of Dirichlet $$L$$-functions of all even primitive characters of conductor at most $$Q$$, where $$Q$$ is a parameter tending to infinity. For $$X=Q^{\eta }$$ with $$1<\eta <2$$, we examine Dirichlet polynomials of length $$X$$ with coefficients those of the Dirichlet series of a product of an arbitrary (finite) number of shifted $$L$$-functions from the family. Assuming the Generalized Lindelöf Hypothesis for Dirichlet $$L$$-functions, we prove an asymptotic formula for averages of these Dirichlet polynomials. Our result agrees with the prediction of the recipe of Conrey, Farmer, Keating, Rubinstein, and Snaith for these averages. One may view our result as evidence for the “one-swap” terms in the recipe prediction for the general $2k$th moment of the family of Dirichlet $$L$$-functions. 
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    Free, publicly-accessible full text available February 1, 2026
  2. ; ; ; (, Acta Arithmetica)
    Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least 67.9% of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery’s theorem and show how to apply it to prove the following result on simple zeros: If all the zeros ρ=β+iγ of the Riemann zeta-function such that T3/8<γ≤T satisfy ∣∣β−1/2∣∣<1/(2logT), then, as T tends to infinity, at least 61.7% of these zeros are simple. The method of proof neither requires nor provides any information on whether any of these zeros are or are not on the critical line where β=1/2. We also obtain the same result under the weaker assumption of a strong zero-density hypothesis. 
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  3. ; ; (, Journal of Mathematical Analysis and Applications)
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  4. ; ; (, Mathematical Research Letters)
    null (Ed.)
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  5. ; ; (, Inventiones mathematicae)
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