Distribution of integers with prescribed arithmetic structure and applications

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Copyright: Yau, Kam Hung
Abstract
This thesis contains results about the distribution of integers with prescribed arithmetic structure and an application. These include a counting problem in Diophantine approximation, an asymptotic formula for the number of solutions to congruence's with certain arithmetic conditions, lower bounds on the number of smooth square-free integers in arithmetic progression, an estimate on the smallest square-full number in almost all residue classes modulo a prime, a relaxation of Goldbach's conjecture from the point of view of Ramare's local model, and lastly a refinement of the classical Burgess bound.
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Author(s)
Yau, Kam Hung
Supervisor(s)
Shparlinski, Igor E.
Zhao, Liangyi
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Publication Year
2020
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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download public version.pdf 1.52 MB Adobe Portable Document Format
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