Number Theory Seminar

Speaker: Tiago Fonseca (Paris-Sud Orsay).

Title: Higher Ramanujan equations and periods of abelian varieties.

Abstract: The Ramanujan equations are certain algebraic differential equations satisfied by the classical Eisenstein series E_2, E_4, E_6. These equations play a pivotal role in the proof of Nesterenko's celebrated theorem on the algebraic independence of values of Eisenstein series, which gives in particular a lower bound on the transcendence degree of fields of periods of elliptic curves. Motivated by the problem of extending Nesterenko's transcendence methods to other settings, we shall explain how to generalize Ramanujan's equations to higher dimensions via a geometric approach, and how the values of a particular solution of these equations relate with periods of abelian varieties.

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