Number Theory Seminar

Tuesday, October 4, 2022 2:30 pm - 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

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Meeting ID: 992 3965 9097

Passcode: 846449