We present a method to determine Frobenius elements in arbitrary Galois extensions of global fields, which may be seen as a generalisation of Euler’s criterion. It is a part of the general question how to compare splitting fields and identify conjugacy classes in Galois groups, which we will discuss as well.
Tim Dokchitser. Vladimir Dokchitser. "Identifying Frobenius elements in Galois groups." Algebra Number Theory 7 (6) 1325 - 1352, 2013. https://doi.org/10.2140/ant.2013.7.1325