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13. Apr 2023

The density of polynomials of degree n over Zp that have exactly r roots in Qp

Algebraic Geometry and Number Theory Seminar

Datum: 13. April 2023 | 13:00 – 15:00
Sprecher: Stevan Gajovic , MPIM Bonn
Veranstaltungsort: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Sprache: Englisch

Let f be a random polynomial in Zp[x] of degree n. We determine the density of such polynomials f having 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 and some asymptotic results. This is joint work with Manjul Bhargava, John Cremona, and Tom Fisher.

 

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Datum:
13. April 2023
13:00 – 15:00

Sprecher:
Stevan Gajovic , MPIM Bonn

Veranstaltungsort:
Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA

Sprache:
Englisch

Ansprechpartner:

Birgit Oosthuizen-Noczil

Email:
birgit.oosthuizen-noczil@ist.ac.at

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