SUM-PRODUCT ESTIMATES APPLIED TO WARING’S PROBLEM MOD P

Abstract. 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 th