Date of Award
8-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Neil Calkin
Committee Member
William Bridges
Committee Member
Matthew Saltzman
Committee Member
Keri Ann Sather-Wagstaff
Abstract
This dissertation explores fundamental conjectures in number theory, focusing on the distribution patterns of representation functions in prime pairs. The work concentrates on twin primes, cousin primes, and primes separated by six units, offering a fresh heuristic interpretation of the Hardy-Littlewood correction factor. The analysis progresses to investigate the partition function for prime pairs in the form $(p, p+k)$, specifically for $k = 2, 4, 6$. The study culminates in the derivation of a general formula for prime pairs $(p, p+d)$, where $d$ is an even integer. Drawing on the insights gleaned from examining the correction factor, this dissertation proposes new conjectures about the partition functions of these distinct prime pairs.
Recommended Citation
Wang, Yunan, "Some Experiments in Additive Number Theory" (2024). All Dissertations. 3736.
https://open.clemson.edu/all_dissertations/3736