2 problems

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Expected optimal order for Weyl-sum mean values when $s\geq k$
Let … For $s\geq k\geq3$ , elementary estimates give the lower bound $\mathbf{I}_{s,k}(X)\gg X^{2s-k}$ . Optimal mean-value conjecture. In this range, $\mathbf{I}_{s,k}(X)$ has true…
Conjectureopenanalytic-number-theory vinogradov-mean-values weyl-sumsarXiv posted 2 days ago
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Salem–Wooley paucity conjecture for Vinogradov mean values
Paucity conjecture. If $2\leq s<k$ , the diagonal solutions dominate, so that
Conjectureopenvinogradov-mean-values waring-problem weyl-sumsarXiv posted 2 days ago

Expected optimal order for Weyl-sum mean values when s≥ks\geq ks≥k