All Outputs (2)

Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves (2022)
Journal Article
Dendrinos, S., Hughes, K., & Vitturi, M. (2022). Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves. Journal of Fourier Analysis and Applications, 28(4), Article 69. https://doi.org/10.1007/s00041-022-09958-y

We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages AN along polynomial curves in Z^d. Combined with certain elementary estimates for the number of solutions to certain special systems of diophantine equations,... Read More about Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves.

On the inhomogeneous Vinogradov system (2022)
Journal Article
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

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 Vinogrado...