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Description
Similar to the real numbers, the p-adic fields are completions of the rational numbers. However, distance in this space is determined based on divisibility by a prime number, p, rather than by the traditional absolute value. This gives rise to a peculiar topology which offers significant simplifications for p-adic continuous functions and p-adic integration than is present in the real numbers. These simplifications may present significant advantages to modern physics – specifically in harmonic analysis, quantum mechanics, and string theory. This project discusses the construction of the p-adic numbers, elementary p-adic topology, p-adic continuous functions, introductory p-adic measure theory, the q-Volkenborn distribution, and applications of p-adic numbers to physics. We define q-Volkenborn integration and its connection to Bernoulli numbers.
ContributorsBurgueno, Alyssa Erin (Author) / Childress, Nancy (Thesis director) / Jones, John (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor, Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05