EXPLORING BERNOULLI NUMBERS AND THEIR APPLICATIONS

Date

2024-6

Author

Omar, Ahmed Abdelrazik Badawy Abdelrazik

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In this thesis, we focus on Bernoulli numbers and their applications. We give a brief summary of the theory of p-adic numbers to analyze their practical results. In particular, we focus on p-adic measures and integrals to deepen our comprehension of Bernoulli numbers. A notable application is presenting an alternative proof of Faulhaber’s formula. We review a recent algorithm to calculate Bernoulli numbers for considerably large indices. Furthermore, we also review the class number formula, which serves as the basis for investigating irregular primes that are linked to the numerator of Bernoulli numbers.

Subject Keywords

P-adic numbers, Bernoulli numbers, Faulhaber’s formula, Irregular primes

URI

https://hdl.handle.net/11511/110062

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Graduate School of Natural and Applied Sciences, Thesis