Dipartimento di Matematica "Giuseppe Peano"

Lezione lagrangiana

Some new elliptic integrals

Relatore:
Prof. David Masser 
University of Basel

Data e luogo:
22 novembre 2022 alle 16.30
in Aula Magna del Dipartimento di Matematica "G. Peano"

Abstract 
In 1981 James Davenport surmised that if an algebraic function f(x, t) is not integrable (with respect to x) by elementary means when t is an independent variable, then there are most finitely many complex numbers τ such that f(x, τ ) is integrable by elementary means. In 2020 Umberto Zannier and I obtained a couple of counterexamples and in principle classified all of them with algebraic coefficients (they are somewhat rare). In this talk I will review our work and briefly sketch our recent practical description of all elliptic counterexamples (they are not unrelated to so-called Ribet curves).