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- W2738561158 abstract "Let $I_{s,k,r}(X)$ denote the number of integral solutions of the modified Vinogradov system of equations $$x_1^j+ldots +x_s^j=y_1^j+ldots +y_s^jquad (text{$1le jle k$, $jne r$}),$$ with $1le x_i,y_ile X$ $(1le ile s)$. By exploiting sharp estimates for an auxiliary mean value, we obtain bounds for $I_{s,k,r}(X)$ for $1le rle k-1$. In particular, when $s,kin mathbb N$ satisfy $kge 3$ and $1le sle (k^2-1)/2$, we establish the essentially diagonal behaviour $I_{s,k,1}(X)ll X^{s+epsilon}$." @default.
- W2738561158 created "2017-07-31" @default.
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- W2738561158 date "2017-07-19" @default.
- W2738561158 modified "2023-09-27" @default.
- W2738561158 title "Vinogradov systems with a slice off" @default.
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