Dirichlet Characters

The Dirichlet characters package provides support for computing with the group of homomorphism $(\mbox{\bf Z}/N\mbox{\bf Z})^* \rightarrow R^*$, where R is a ring.

• Dirichlet group over a field K as the set of rational characters from $(\mbox{\bf Z}/N\mbox{\bf Z})^*$ to $\overline{K}^*$.
• Computation of group generators, enumeration of elements, and representatives of Galois-conjugacy classes of characters.
• Construction and evaluation of Dirichlet characters.
• Invariants of characters, such as their conductor, modulus, and order.

Dirichlet characters have been developed in support of the new Hecke module types. Future applications to exponential sums will also be developed.