Abstract
Let [Formula: see text] and [Formula: see text]. We consider the sum [Formula: see text]. Sharp upper bounds are known when [Formula: see text], using continued fractions or the three-distance theorem. However, these techniques do not seem to apply in higher dimension. We introduce a different approach, based on a general counting result of Widmer for weakly admissible lattices, to establish sharp upper bounds for arbitrary [Formula: see text]. Our result also sheds light on a question raised by Lê and Vaaler in 2013 on the sharpness of their lower bound [Formula: see text].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
