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Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 2019-07-16)
In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find their applications in the theory ...
A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences
In 1927, Artin conjectured that any integer other than −1 or a perfect square generates the multiplicative group (Z/pZ)× for infinitely many p. In 2000, Moree and Stevenhagen considered a two-variable version of this ...