L-functions in Magma
Tim Dokchitser
University of Edinburgh
Abstract:
The aim of this talk is to present new functionality in Magma for working
with zeta- and L-functions in geometry and number theory. I will discuss the
built-in functions (the Riemann zeta function, Dedekind zeta function of a
number field, and L-functions of characters, modular forms and elliptic
curves); computing values, derivatives and Taylor expansions of L-functions;
how to construct new L-functions from either the existing ones or by
specifying the Dirichlet coefficients and arithmetic invariants. Finally, I
will give some examples to illustrate what the functions can be used for.