Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs
Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs
We derive an asymptotic formula for the number of solutions in a given subfield to certain system of equations over finite fields. As an application, we construct new families of maximal cliques in generalized Paley graphs. Given integers <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d greater-than-or-equal-to 2"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> …