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2022 On the representation of integers by binary forms defined by means of the relation (x+yi)n=Rn(x,y)+Jn(x,y)i
Anton Mosunov
Mosc. J. Comb. Number Theory 11(1): 71-78 (2022). DOI: 10.2140/moscow.2022.11.71

Abstract

Let F be a binary form with integer coefficients, degree d3 and nonzero 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)CFZ2d 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.

Citation

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Anton Mosunov. "On the representation of integers by binary forms defined by means of the relation (x+yi)n=Rn(x,y)+Jn(x,y)i." Mosc. J. Comb. Number Theory 11 (1) 71 - 78, 2022. https://doi.org/10.2140/moscow.2022.11.71

Information

Received: 4 August 2021; Revised: 19 February 2022; Accepted: 5 March 2022; Published: 2022
First available in Project Euclid: 9 May 2022

Digital Object Identifier: 10.2140/moscow.2022.11.71

Subjects:
Primary: 11D45 , 11D59 , 11E76

Keywords: automorphism group , binary form , fundamental region , representation of integers by binary forms , Thue equation

Rights: Copyright © 2022 Mathematical Sciences Publishers

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