**
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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