Efficient congruencing in ellipsephic sets: the quadratic case
Volume 200 / 2021
Acta Arithmetica 200 (2021), 331-348
MSC: 11A63, 11D45, 11L07, 11P55.
DOI: 10.4064/aa191216-8-2
Published online: 18 October 2021
Abstract
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.
