Quadratic equations over finite fields and class numbers of real quadratic fields (Q1386701)

The authors look at finite fields \(\mathbb{F}_p\), where \(p>2\) is prime, and derive explicit formulae for the number of points of certain quadratic hypersurfaces in \(\mathbb{F}^n_p\), where \(n\in\mathbb{N}\). Furthermore, they show that the class number of \(\mathbb{Q}(\sqrt p)\) for \(p\equiv 1\pmod 4\) can be expressed in terms of their formulae. They conclude the paper with a formula for the validity of the Ankeny-Chowla conjecture to hold for \(\mathbb{Q}(\sqrt p)\).