Igor Wigman: Around Gauss circle problem: Hardy's conjecture and the distribution of lattice points near circles

Abstract.

This talk is based on a joint work with Steve Lester.

We review the Gauss circle problem, and Hardy's conjecture regarding the order of magnitude of the remainder term. It is attempted to rigorously formulate the folklore heuristics behind Hardy's conjecture. Some weaker forms of the likely statement are proved to support it.