Abstract
Let f be any arithmetic function and define Sf(x):=∑n⩽xf([x/n]). When f equals the Euler totient function φ, several authors studied the upper and lower bounds of Sφ(x). In this paper we shall prove that Sφ(x) has an asymptotic formula by the method of exponential sums. This result proves a conjecture proposed by Bordellés, Dai, Heyman, Pan and Shparlinski. Some other asymptotic formulas for arbitrary f are also given in this paper.
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.
