Skip to main content

Research Repository

Advanced Search

On the inhomogeneous Vinogradov system

Brandes, Julia; Hughes, Kevin


Julia Brandes

Kevin Hughes


We show that the system of equations

∑_{i=1}^{s} (x_i^j−y_i^j) = a_j (1⩽j⩽k)

has appreciably fewer solutions in the subcritical range s<k(k+1)/2
than its homogeneous counterpart, provided that a_ℓ≠0 for some ℓ⩽k−1. Our methods use Vinogradov’s mean value theorem in combination with a shifting argument.


Brandes, J., & Hughes, K. (2022). On the inhomogeneous Vinogradov system. Bulletin of the Australian Mathematical Society, 106(3), 396-403.

Journal Article Type Article
Acceptance Date Feb 15, 2022
Online Publication Date Apr 19, 2022
Publication Date 2022-12
Deposit Date Dec 2, 2022
Publicly Available Date Dec 2, 2022
Journal Bulletin of the Australian Mathematical Society
Print ISSN 0004-9727
Electronic ISSN 1755-1633
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 106
Issue 3
Pages 396-403
Keywords Diophantine equations, exponential sums
Public URL


You might also like

Downloadable Citations