My work has been devoted to developing an arithmetic analogue of differential equations.

One of my main ideas was to replace derivatives of functions by Fermat quotients of numbers.

This led to the discovery new analogies between numbers and functions and to applications of ideas from function theory to number theory.

I am the author of 5 research monographs and 94 research papers.

I am extremely honored by my recent promotion and I am deeply grateful to my colleagues and to UNM for the excellent research environment.