Gabriel A. Dill (Universität Bonn): The Modular Support Problem

Herr Gabriel A. Dill (Universität Bonn)

The Modular Support Problem

Abstract:
In 1988, Erdös asked: let a and b be positive integers such that for all n, the set of primes dividing aⁿ − 1 is equal to the set of primes dividing bⁿ − 1. Is a = b? Corrales and Schoof answered this question in the affirmative and showed more generally that, if every prime dividing aⁿ − 1 also divides bⁿ − 1, then b is a power of a.

In joint work that was inspired by the analogy between roots of unity and singular moduli, i.e. j-invariants of elliptic curves with complex multiplication, Francesco Campagna and I have studied this so-called support problem with the Hilbert class polynomials H_D(T ) instead of the polynomials Tⁿ − 1.

In this talk, I will introduce singular moduli, Hilbert class polynomials, and the analogy with roots
of unity and present the results we obtained.

Vor diesem Vortrag, ab 16.45 Uhr, gibt es wieder Kaffee und Tee im Raum 1404.
Es sind alle herzlich dazu eingeladen.