Lattice points in a circle for generic unimodular shears

2015/08/03 by Kelmer, Dubi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1508.00487

Abstract

Given a unimodular lattice Λ⊆ ℝ² consider the counting function N_Λ(T) counting the number of lattice points of norm less than T, and the remainder R_Λ(T)=N(T)-πT². We give an elementary proof that the mean square of the remainder over the set of all shears of a unimodular lattice is bounded by O(Tlog²(T)).

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