Weil integration

Weil integration is a mathematical method used to integrate functions over a specific type of geometric object called a p-adic manifold, which arises in number theory and algebraic geometry. Unlike standard calculus, Weil integration considers functions defined on spaces related to solutions of polynomial equations over p-adic numbers—extensions of the rational numbers that focus on divisibility by a prime number p. This technique allows mathematicians to analyze complex algebraic structures by assigning measures (or sizes) to these spaces and integrating functions accordingly, aiding in the study of arithmetic properties and number-theoretic problems.