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An algorithmic solution to the representation problem for definite binary quadratic forms
Jameson, Eric Joseph
Interlando, J. CarmeloO'Sullivan, MichaelEckberg, Carl
xiii, 70 pages : illustrations
This thesis will examine the theory of binary quadratic forms. Specifically, it will develop a series of algorithms which will be able to solve the representation problem for binary quadratic forms of negative discriminant. First, we must introduce several definitions and prove several results involving binary quadratic forms. Then we turn our focus to constructing forms of a given discriminant and leading coefficient. Finally, we use the reduction of binary quadratic forms in order to determine solutions of the representation problem. Based upon these results, we are able to provide insight in a future direction of how to generalize these algorithms to all binary quadratic forms.
Applied Mathematics with a concentration in Mathematical Theory of Communication Systems
Mathematics and Statistics
San Diego State University
Master of Science (M.S.) San Diego State University, 2016
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