Gandalf (Pure Maths Student Seminar): Arithmetic & Denominators of Eisenstein Series
8 June 2016 16:00 in CM221
A modular form f(z) for SL_2(Z) with rational coefficieints has a denominator, ie an integer D exists such that Df(z) has integral coefficients; this D is often arithmetically interesting - in particular, when f(z) is an Eisenstein series.
Any modular form f(z) has an associated cohomology class for the space H/SL_2(Z), which will also have a 'de Rham denominator'; we hope that these two denominators are in fact the same!
By an extension of the classical Shintani lift, I shall try to explain a method (so far only partially successful) in showing this conjecture. We give an overview of the methods used, as well as a couple of generalisations that I have been looking at this year. The talk should hopefully give an idea of the enormous arithmetic interest in the area of modular forms, as well as the way that geometric methods may be used in the pursuit of number-theoretic goals.
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.