p-adic differential equation

A **p-adic differential equation** is a differential equation in which the role of the real numbers is played by the field of p-adic numbers for some prime $p$.

According to Kedlaya 10, the study of zeta functions via $p$-adic analysis lends itself much more readily to numerical computation than do methods employing étale cohomology:

…it is not straightforward to describe étale cohomology to a computer well enough that the computer can make calculations. (Kedlaya 10, p.5)

- Kiran Kedlaya,
*p-adic Differential Equations*, CUP, 2010, (doi)