Staff Profile
Mr Jonathan Crawford
I am currently a PhD student under the supervision of Jens Funke, having previously completed my MMath at the University Of Warwick (where my 4th year project was on p-adic Riemann zeta functions and p-adic Eisenstein series under David Loeffler).
My research area is number theory, and more specifically I am currently trying to adapt the work of Martin Hövel "Automorphe Formen mit Singularitäten auf dem hyperbolischen Raum" which describes how to construct a twisted theta lift of (vector-valued) harmonic weak Maass forms of weight 1/2 to \Gamma_{0}(N)-invariant automorphic forms on the upper-half plane, as well as the close relationship with the Shimura lift.
I adapt this lift to forms of weight k-3/2 for k an integer, lifting to weight 2-2k automorphic forms in \Gamma_{0}(N) on the upper half-plane, which are in fact locally harmonic Maass forms as described by Bringmann, Kane and Kohnen. Using vector-valued harmonic weak Maass forms will mean this twisted theta lift will also form a generalisation to any level of the closely related lifts described by Bringmann, Kane and Viazovska and an extension in the case of signature (2,1) of the Borcherds lift.
Research Interests
- Number Theory