2021/08/23 by Quesada-Herrera, Emily
#11M06 #11M26 #41A30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2108.10238
We study the q-analogue of the average of Montgomery's function F(α, 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.