Michael A. Bennett
University of British Columbia
Publication
Featured researches published by Michael A. Bennett.
Canadian Journal of Mathematics | 2004
Michael A. Bennett; Chris M. Skinner
In this paper, we develop techniques for solving ternary Diophantine equations of the shape Ax n + By n = Cz 2 , based upon the theory of Galois representations and modular forms. We subse- quently utilize these methods to completely solve such equations for various choices of the parameters A, B and C. We conclude with an application of our results to certain classical polynomial-exponential equations, such as those of Ramanujan-Nagell type.
Ramanujan Journal | 2002
Mark Bauer; Michael A. Bennett
AbstractIn this paper, we refine work of Beukers, applying results from the theory of Padé approximation to (1 − z)1/2 to the problem of restricted rational approximation to quadratic irrationals. As a result, we derive effective lower bounds for rational approximation to
Proceedings of The London Mathematical Society | 2006
Michael A. Bennett; Nils Bruin; Kalman Gyory; Lajos Hajdu
Transactions of the American Mathematical Society | 2001
Michael A. Bennett
\sqrt m
Compositio Mathematica | 2004
Michael A. Bennett; Vinayak Vatsal; Soroosh Yazdani
Canadian Journal of Mathematics | 2001
Michael A. Bennett
(where m is a positive nonsquare integer) by rationals of certain types. Forexample, we have
Bulletin of The London Mathematical Society | 2004
Michael A. Bennett
International Journal of Number Theory | 2010
Michael A. Bennett; Jordan S. Ellenberg; Nathan Ng
\left| {\sqrt 2 - \frac{p}{q}} \right| \gg q^{ - 1.47} {\text{ and }}\left| {\sqrt 3 - \frac{p}{q}} \right| \gg q^{ - 1.62}
Journal of The Australian Mathematical Society | 1997
Michael A. Bennett
Compositio Mathematica | 2006
Michael A. Bennett; Kalman Gyory; Maurice Mignotte; Ákos Pintér
provided q is a power of 2 or 3, respectively. We then use this approach to obtain sharp bounds for the number of solutions to certain families of polynomial-exponential Diophantine equations. In particular, we answer a question of Beukers on the maximal number of solutions of the equation x2 + D = pn where D is a nonzero integer and p is an odd rational prime, coprime to D.