Computational Algebra Seminar: Watkins -- L-function computations

Speaker: Mark Watkins (Sydney)
Title: L-function computations; theory and practice
Time & Place: 3-4pm, Thursday 22 Jan, Carslaw 535.

Abstract: I will describe how L-functions can be attached to various
number theoretic objects, and comment on the motivation for wanting to
compute with these L-functions, in particular what types of conjectures
they are supposed to obey. Then I will give some specific examples
from work that has derived from an NSF Focused Research Group grant,
particularly some experiments with rank 4 quadratic twists, and some
appearances of eta-quotients with Waldspurger lifts of modular forms.
With the latter, in some examples it is possible to write the q-series as
a product of two weighted theta series, and then the use of FFT convolution
can be used to get a large initial segment (up to 10^10 in some cases).