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math.NT2026
The variance of the number of lattice points in narrow sectors
Stephen Lester, Ezra Waxman, Nadav Yesha
We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding…
math.NT2026
Average analytic rank for the -functions of the elliptic curves
Chantal David, Lucile Devin, Alessandro Fazzari +1
We study the average analytic rank in the family of -functions associated with the elliptic curves , as varies over fourth-power-free odd integ…