The Fourier coefficients of cuspidal modular forms are subtle invariants which contain a wealth of arithmetic information. Even bounding the size of these coefficients involve very deep mathematics -- the best bounds follow from Deligne's proof of the Weil conjectures. In this talk, rather than looking at complex absolute values, we will instead focus on the p-adic size of p-th Fourier coefficient of an eigenform. We give a conjectural description of the variation of these sizes over all weights (classical and p-adic). This conjecture (the ghost conjecture) then has implications regarding the shape and structure of the eigencurve. This is a joint project with John Bergdall.
Donnerstag, den 30. November 2017 um 17.15 Uhr, in Mathematikon INF 205, Hörsaal Mathematikon Donnerstag, den 30. November 2017 at 17.15, in Mathematikon INF 205, Hörsaal Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. G. Böckle