On the error term of a lattice counting problem

JOURNAL OF NUMBER THEORY

卷:182

Article

Bordelles, Olivier¹  Luca, Florian^2,3,4  Shparlinski, Igor E.⁵ 

[1] 2 Allee Combe, F-43000 Aiguilhe, France

[2] Univ Witwatersrand, Sch Math, Private Bag X3, ZA-2050 Johannesburg, South Africa

[3] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[4] Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, CZ-70103 Ostrava 1, Czech Republic

[5] Univ New South Wales, Dept Pure Math, Sydney, NSW 2052, Australia

关键词: Lattices;    Farey fractions;    Vaaler polynomials;   

DOI  :  10.1016/j.jnt.2017.07.019

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free