Posted in

Speaker:

Julie Desjardins
Affiliation:

MPIM
Date:

Wed, 2017-10-11 16:30 - 17:30
Location:

MPIM Lecture Hall Let f be a primitive separable polynomial of positive degree in Z[x]. It is conjectured that a positive proportion of the

values are square-free. This is known as the square-free conjecture. In 1953, Erdös showed that for cubics there are

infinitely many square-free values, and in 1967, Hooley gave the result about positive density when $\deg=3$. Although

we know that is suffices to check the conjecture for the factors, it is still not know for irreducible polynomials of degree

greater than $3$. In $h$ variables, Greaves proves the conjecture for degree $\leq 3h$.

In this talk, we relate this problem to its main motivation: the study of the variation of the analytic rank in a family

of elliptic curves.

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |