Outputs (5)

A polynomial Zsigmondy theorem (2011)
Journal Article
Flatters, A., & Ward, T. (2011). A polynomial Zsigmondy theorem. Journal of Algebra, 343(1), 138-142. https://doi.org/10.1016/j.jalgebra.2011.07.010

We find an analogue of the primitive divisor results of Bang and Zsigmondy in polynomial rings.

A repulsion motif in Diophantine equations (2011)
Journal Article
Everest, G., & Ward, T. (2011). A repulsion motif in Diophantine equations. The American Mathematical Monthly, 118(7), 584-598. https://doi.org/10.4169/amer.math.monthly.118.07.584

Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a non-singular plane cubic equation has... Read More about A repulsion motif in Diophantine equations.

A directional uniformity of periodic point distribution and mixing (2011)
Journal Article
Miles, R., & Ward, T. (2011). A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems - Series A, 30(4), 1181-1189. https://doi.org/10.3934/dcds.2011.30.1181

For mixing Z^d-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown... Read More about A directional uniformity of periodic point distribution and mixing.

An introduction to Number Theory (2011)
Book
Everest, G., & Ward, T. (2011). An introduction to Number Theory. Science Press, Beijing

Mertens' theorem for toral automorphisms (2011)
Journal Article
Jaidee, S., Stevens, S., & Ward, T. (2011). Mertens' theorem for toral automorphisms. Proceedings of the American Mathematical Society, 139(05), 1819-1824. https://doi.org/10.1090/s0002-9939-2010-10632-9

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer, periodic orbit... Read More about Mertens' theorem for toral automorphisms.