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The solution to Hilbert's tenth problem.Cooper, Sarah Frances January 1972 (has links)
No description available.
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Thue equations and related topicsAkhtari, Shabnam 11 1900 (has links)
Using a classical result of Thue, we give an upper bound for the number of solutions to a family of quartic Thue equations. We also give an upper bound upon the number of solutions to a family of quartic Thue inequalities. Using the Thue-Siegel principle and the theory of linear forms in logarithms, an upper bound is given for general quartic Thue equations. As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX⁴ - bY² = 1, for fixed positive integers a and b, possesses at most two solutions in positive
integers X and Y. Since there are infinitely many pairs (a, b) for which two
such solutions exist, this result is sharp. It is also effectively proved that
for fixed positive integers a and b, there are at most two positive integer
solutions to the quartic Diophantine equation
aX⁴ - bY² = 2.
We will also study cubic and quartic Thue equations by combining some classical methods from Diophantine analysis with modern geometric ideas.
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Number of classes of solutions of the equation x2-Dy2=4E /Lemire, Mathieu, January 1900 (has links)
Thesis (M. Sc.)--Carleton University, 2003. / Includes bibliographical references (p. 143-145). Also available in electronic format on the Internet.
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The null forms Ax²By²Cz²Du²which represent all integers ...Brixey, John Clark, Unknown Date (has links)
Thesis (Ph. D.)--University of Chicago, 1936. / Vita. Lithoprinted. "Private editions, distributed by the University of Chicago libraries Chicago, Illinois."
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Some explicit estimates on linear diophantine equations in three prime variables /Choi, Kwok-kwong, Stephen. January 1990 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1991.
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Diophantine problems in function fields of positive characteristic /Jeong, Sang Tae, January 1999 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 63-65). Available also in a digital version from Dissertation Abstracts.
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Eduard Warings Meditationes algebraicæMayer, Franz Xaver. January 1923 (has links)
Inaug.-diss.--Universität Zürich. / Lebenslauf. Bibliographical foot-notes.
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On Lang's diophantine conjecture for surfaces of general type /Kang, Cong Xuan, January 1999 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 20-22). Available also in a digital version from Dissertation Abstracts.
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Thue equations and related topicsAkhtari, Shabnam 11 1900 (has links)
Using a classical result of Thue, we give an upper bound for the number of solutions to a family of quartic Thue equations. We also give an upper bound upon the number of solutions to a family of quartic Thue inequalities. Using the Thue-Siegel principle and the theory of linear forms in logarithms, an upper bound is given for general quartic Thue equations. As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX⁴ - bY² = 1, for fixed positive integers a and b, possesses at most two solutions in positive
integers X and Y. Since there are infinitely many pairs (a, b) for which two
such solutions exist, this result is sharp. It is also effectively proved that
for fixed positive integers a and b, there are at most two positive integer
solutions to the quartic Diophantine equation
aX⁴ - bY² = 2.
We will also study cubic and quartic Thue equations by combining some classical methods from Diophantine analysis with modern geometric ideas. / Science, Faculty of / Mathematics, Department of / Graduate
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Diophantine inequalities in fields of formal laurent power series /Aggarwal, Satish Kumar January 1965 (has links)
No description available.
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