Posted in

Speaker:

Stevan Gajovic
Affiliation:

MPIM
Date:

Wed, 12/10/2022 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

Let f be a random polynomial in Zp[x] of degree n. We determine

the density of such polynomials f that have exactly r roots in Qp. We also

determine the expected number of roots of monic polynomials f in Zp[x] of

degree n, and, more generally, the expected number of sets of exactly d

elements consisting of roots of such f. We show that these densities are

rational functions in p and discuss the remarkable symmetry phenomenon that

occurs. This is joint work Manjul Bhargava, John Cremona, and Tom Fisher.

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