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An Isaac Newton Institute Workshop

Random Matrix Theory and Arithmetic Aspects of Quantum Chaos

On the number of lattice points in a thin annulus

Author: Christopher Hughes (AIM)

Abstract

We count the number of integer lattice points in an annulus of inner-radius $t$ and outer-radius $t+\rho$. If $\rho \to 0$ sufficiently slowly then the distribution of this counting function as $t\to\infty$ weakly converges to the normal distribution.