Mathematics

Fixing q prime, we say 1 ≤ a < q is a quadratic nonresidue if there is no integer solution to the congruence x² ≡ a mod q. For more than a century number theorists have worked on finding estimates of the size of the least quadratic nonresidue. In this talk we will review some facts about quadratic residues and show how with the aid of the Generalized Riemann Hypothesis we can employ the framework of Fourier Optimization to improve the best known asymptotic bounds on the least quadratic nonresidue. Based on joint work with E. Carneiro, M. Milinovich, and E. Quesada-Herrera.