## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, October 17, 2018 — 12:30 PM EDT

**Anton Mosunov, Department of Pure Mathematics, University of Waterloo**

"Representation of Prime Powers by Binary Forms"

*The PhD Student Research Seminar is an opportunity to share your research progress with your fellow students. Hopefully we will each be more aware of the various research areas in our department, and maybe even find connections that we did not notice before. Works-in-progress and technical presentations are welcome and encouraged. Let's share and get to know our peers! Also there will be cookies.*

Consider an irreducible polynomial *f*(*x*) of degree *d*>=7, with integer coefficients. Suppose that it has the following interesting property: if *a* is a root of *f*(*x*) then the field *Q*(*a*) contains all roots of *f*(*x*). Let *F*(*x*,*y*) be its homogenization. I will explain why every sufficiently large prime power gets represented by |*F*(*x*,*y*)| at most 12 times, as long as *x* and *y* are coprime.

MC 5417

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1