An asymptotic formula with square root error term counts elements of given norm and trace in finite semisimple algebras over finite fields, extending commutative results to non-commutative cases.
Eichler, Allgemeine Kongruenz-Klasseneinteilungen der Ideale einfacher Algebren über algebraischen Zahlkör- pern und ihre L-Reihen.J
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Norm-trace and Kloosterman sums in finite semi-simple algebras
An asymptotic formula with square root error term counts elements of given norm and trace in finite semisimple algebras over finite fields, extending commutative results to non-commutative cases.