PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Efficient congruencing in ellipsephic sets: the quadratic case

Volume 200 / 2021

Kirsti D. Biggs Acta Arithmetica 200 (2021), 331-348 MSC: 11A63, 11D45, 11L07, 11P55. DOI: 10.4064/aa191216-8-2 Published online: 18 October 2021


We bound the number of solutions to a quadratic Vinogradov system of equations in which the variables are required to satisfy digital restrictions in a given base. Certain sets of permitted digits, namely those giving rise to few representations of natural numbers as sums of elements of the digit set, allow us to obtain better bounds than would be possible using the size of the set alone.


  • Kirsti D. BiggsMathematical Sciences
    University of Gothenburg and Chalmers Institute of Technology
    412 96 Göteborg, Sweden

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image