p-Adic Numbers with an Emphasis on q-Volkenborn Integration
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.
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2020-05
Agent
- Author (aut): Burgueno, Alyssa Erin
- Thesis director: Childress, Nancy
- Committee member: Jones, John
- Contributor (ctb): School of Mathematical and Statistical Sciences
- Contributor (ctb): Department of Physics
- Contributor (ctb): School of Mathematical and Statistical Sciences
- Contributor (ctb): School of Mathematical and Statistical Sciences
- Contributor (ctb): Barrett, The Honors College