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

Herr Gabriel A. Dill (Universität Bonn)

The Modular Support Problem

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 HD(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.

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