## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, October 4, 2022 — 2:30 PM EDT

**Anton Mosunov, Department of Pure Mathematics, University of Waterloo
“On the Representation of Integers by Binary Forms Defined
by Means of the Relation (x + yi)n = Rn(x, y) + Jn(x, y)i”**

Let F be a binary form with integer coefficients, degree d ≥ 3 and non-zero discriminant. Let

RF (Z) denote the number of integers of absolute value at most Z which are represented by F. In

2019 Stewart and Xiao proved that RF (Z) ∼ CFZ2/d for some positive number CF . We compute CRn

and CJn for the binary forms Rn(x, y) and Jn(x, y) defined by means of the relation

(x + yi)n = Rn(x, y) + Jn(x, y)i,

where the variables x and y are real.

MC 5479 and Zoom

Zoom Info:

https://uwaterloo.zoom.us/j/99239659097?pwd=ZjNVRjQ1MWpuQmhTb01ZS0RGNDJjQT09

Meeting ID: 992 3965 9097

Passcode: 846449

Event tags

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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

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