P-Adic Analysis

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Focusing on p-adic analysis and number theory, this work presents recent advancements made by mathematicians over the past five years. It begins with foundational concepts, including the construction of p-adic numbers and power series, before delving into the properties of p-adic Dirichlet L-series through p-adic measures. The text introduces p-adic gamma functions and examines their connections to L-series, emphasizing parallels with complex analysis. Additionally, it proves a formula for Gauss sums related to p-adic gamma functions, making it valuable for graduate students and researchers in relevant fields.