Abstract
The aim of the present paper is to generalize earlier work by Thuswaldner and Tichy on Waring's problem with digital restrictions to systems of digital restrictions. Let sq (n) be the q-adic sum of digits function and let d, s, al, ml , ql ∈ N. Then for s > d2(log d + log log d + O (1)) there exists N0 ∈ N such that each integer N ≥N0 has a representation of the form N = xd 1 + ˙ ˙ ˙ + xd s where sql(xi) ≡ al mod ml (1≤ i ≤ s and 1≤ l ≤ L). The result, together with an asymptotic formula of the number of this representations, will be shown with the help of the circle method together with exponential sum estimates.
Sign-in/Register to access full text options 
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.
