Author

T. Wooley

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Preprint Oct 2026

Sharp mean value estimates in the absence of translation-dilation invariance

We establish sharp mean value estimates for various exponential sums lacking translation-dilation invariance properties. For example, suppose that $k\ge 1$ and $s>0$. Then, for each $\varepsilon>0$, one has \[ \int_{[0,1)^k}\biggl| \sum_{1\le h\le X}\sum_{1\le z\le X}e(hz\alpha_1+\ldots +hz^k\alpha_k)\biggr|^{2s}\,{\rm...

T. Wooley · 0 citations

Preprint Oct 2026

The main conjecture for a Vinogradov subsystem

When $k\ge 2$ and $s>0$, we establish that for each $\varepsilon>0$, one has \[ \int_{[0,1)^{k-1}}\biggl| \sum_{1\le x\le X}e(\alpha_2x^2+\ldots +\alpha_k x^k)\biggr|^{2s}\,{\rm d}\boldsymbol \alpha \ll X^{s+\varepsilon}+X^{2s-(k^2+k-2)/2}, \] confirming the main conjecture for a new family of exponential sums beyond t...

T. Wooley · 1 citation