The 2009 Serge Lang Undergraduate Lecture will be delivered by Benedict H. (Dick) Gross on November 5, 2009.
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.