Type: Seminar

Distribution: World

Expiry: 22 Jan 2009

Auth: billu@renoir.maths.usyd.edu.au

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).