Quadratic nonresidues below the Burgess bound
Quadratic nonresidues below the Burgess bound
For any odd prime number [Formula: see text], let [Formula: see text] be the Legendre symbol, and let [Formula: see text] be the sequence of positive nonresidues modulo [Formula: see text], i.e. [Formula: see text] for each [Formula: see text]. In 1957, Burgess showed that the upper bound [Formula: see …