Sum - Product Estimates Applied to Waring ’ S Problem Mod


Let γ(k, p) denote Waring’s number (mod p) and δ(k, p) denote the ± Waring’s number (mod p). We use sum-product estimates for |nA| and |nA − nA|, following the method of Glibichuk and Konyagin, to estimate γ(k, p) and δ(k, p). In particular, we obtain explicit numerical constants in the Heilbronn upper bounds: γ(k, p) ≤ 83 k, δ(k, p) ≤ 20 k for any positive… (More)


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