Newform Eisenstein congruences of local origin

Abstract: The theory of Eisenstein congruences dates back to Ramanujan’s surprising discovery that the Fourier coefficients of the discriminant function are congruent to the 11th power divisor sum modulo 691. This observation can be explained via the congruence of two modular forms of weight 12 and level 1; the discriminant function and the Eisenstein series, E_{12}. Eisenstein congruences were later used by Ribet in his proof of the converse to Herbrand's theorem. In this talk, I will first discuss the steps Ribet used in his proof and then compare these steps to work in my thesis on congruences between Eisenstein series and newforms of weight k > 2, squarefree level and non-trivial character.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.