On the error term of a lattice counting problem, II

2017/08/24 by Bordellès, Olivier
#11L07 #11L15 #11P21 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.07317

Abstract

Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of polynomials and a device due to Popov allowing us to get an improved main term in the sums of certain fractional parts of polynomials.

Related

• On the error term of a lattice counting problem
• Uniform bounds for lattice point counting and partial sums of zeta functions
• On a generalization of a theorem of Popov
• Effective Counting and Spiralling of Lattice Approximates
• Counting in generic lattices and higher rank actions