Heilbronn's conjecture on Waring's number (mod \(p\))
Let \(p\) be an odd prime number and \(H\) a subgroup of index \(d\) of \(\mathbb{Z}/p\mathbb{Z}\). The authors compute the ``\(g\)'' of the Waring's problem for the \(k =(p-1)/d\)-th powers when \(\Phi(d)=2\) and bound above \(g^q/k\), where \(q\) does not exceed \(\Phi(d),\) by a constant depending only on \(q\). For example it is proved that \(g(k,p)=a-1\) when \(d=4\) and the prime \(p\) is decomposed as \(p=(a+bi)(a-bi).\)
scientific article; zbMATH DE number 5190744