MUSA and the Department of Mathematics, University of California, Berkeley, present

The 2009 Serge Lang Undergraduate Lecture
Benedict H. (Dick) Gross
Department of Mathematics
Harvard University

"The real and p-adic lives of n!"
November 5, 2009
60 Evans - 4:10-5:00pm

Abstract: To study the size of n! = n · (n − 1) · (n − 2) · · · 3 · 2 · 1, it is helpful to have an extension of the function n → n! to the real numbers. Euler found a wonderful extension—the Gamma function.
I’ll discuss this function, and also an analogous function that extends n! to a continuous function on the p-adic integers. I’ll end with some remarks on the connection between the values of these two functions at rational numbers.