Commit 2024-05-01 18:08 17f6b37d
View on Github →feat(NumberTheory/DirichletCharacter): vanishing of Gauss sums when add char is imprimitive (#12324)
The aim of this PR is to show that gaussSum χ e
, for χ
a Dirichlet character mod N
and e
an additive character mod N
, is zero if χ
is primitive but e
is not. This will be used to prove the functional equation for Dirichlet L-series in a later PR.
Along the way we add various general-purpose lemmas about divisibility in ZMod N
and other finite rings, and about conductors and primitivity of Dirichlet and additive characters.