Explicit class field theory for rational function fields
Explicit class field theory for rational function fields
Developing an idea of Carlitz, I show how one can describe explicitly the maximal abelian extension of the rational function field over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper F Subscript q"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{{\mathbf {F}}_q}</mml:annotation> </mml:semantics> …