On the error term of a lattice counting problem

2017/05/24 by Luca, Florian, Shparlinski, Igor E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1705.08714

Abstract

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums coupled with the use of Vaaler polynomials.

Related

• On the error term of a lattice counting problem, II
• Uniform bounds for lattice point counting and partial sums of zeta functions
• On a generalization of a theorem of Popov
• On the best possible exponent for the error term in the lattice point counting problem on the first Heisenberg group
• On the mean square of the error term for the number of lattice points in a two-dimensional area