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arXiv · 2108.10238

On the $q$-analogue of the pair correlation conjecture via Fourier optimization

Emily Quesada-Herrera
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Abstract

We study the $q$-analogue of the average of Montgomery's function $F(\alpha, T)$ over bounded intervals. Assuming the Generalized Riemann Hypothesis for Dirichlet $L$-functions, we obtain upper and lower bounds for this average over an interval that are quite close to the pointwise conjectured value of 1. To compute our bounds, we extend a Fourier analysis approach by Carneiro, Chandee, Chirre, and Milinovich, and apply computational methods of non-smooth programming.

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Emily Quesada-Herrera. 2021-08-23. On the $q$-analogue of the pair correlation conjecture via Fourier optimization. https://arxiv.org/abs/2108.10238

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