Research Output
On the inhomogeneous Vinogradov system
  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 sthan 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.

  • Type:

    Article

  • Date:

    19 April 2022

  • Publication Status:

    Published

  • Publisher

    Cambridge University Press (CUP)

  • DOI:

    10.1017/s0004972722000284

  • Cross Ref:

    10.1017/s0004972722000284

  • ISSN:

    0004-9727

  • Funders:

    Historic Funder (pre-Worktribe)

Citation

Brandes, J., & Hughes, K. (2022). On the inhomogeneous Vinogradov system. Bulletin of the Australian Mathematical Society, 106(3), 396-403. https://doi.org/10.1017/s0004972722000284

Authors

Keywords

Diophantine equations, exponential sums

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