Award Date

1-1-2002

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Arthur Baragar

Number of Pages

63

Abstract

The Rosenberger equations are equations of the form: ax 2 + by2 + cz 2 = dxyz, where the sets of coefficients ( a, b, c, d) are all integers such that each of a, b, and c divides d, and the equations themselves have infinitely many integer solutions. Rosenberger has shown that there are only six such sets of coefficients, one of which is the Markoff equation, x2 + y2 + z2 = 3xyz. Zagier investigated the asymptotic behavior of the integer solutions of the Markoff equation. In this paper, we apply Zagier's techniques to the Rosenberger equations and show that the number N(T) of positive integer solutions that are bounded by T is N(T) = C(log T) 2 + O(log T(log log T) 2), where C is an explicitly computable constant that depends on the equation.

Keywords

Asymptotic; Behavior; Equations; Integer; Rosenberger; Solutions

Controlled Subject

Mathematics

File Format

pdf

File Size

1402.88 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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