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The 17th Annual Charles R. DePrima Memorial Benedict Gross Extending N! to functions on the real and padic numbers, and their values at rational arguments Abstract: I will discuss some functions which extend N! to the real and padic numbers. The first is Euler's Gamma function, and the second is a padic analog defined by Morita. The values of these functions at rational arguments with denominator N are related to the periods and the number of points (mod p) on the Fermat curve xN + yN = 1. Benedict Gross, the George Vasmer Leverett Professor of Mathematics, received his A.B. and Ph.D. degrees from Harvard, and taught at Princeton and Brown before joining the Harvard faculty in 1985. He has served as chair of the Department of Mathematics, and as a member of the Standing Committee on the Core Curriculum, the Educational Policy Committee, and the Committee on Admissions and Financial Aid. Among his many awards and honors are the Cole Prize from the American Mathematical Society, and a MacArthur Fellowship (198691). Gross is known for his work in number theory, particularly the GrossZagier theorem on Lfunctions of elliptic curves with Don Zagier.
The Charles R. DePrima Memorial Undergraduate Mathematics Lecture was established by a gift from Charles R. DePrima and Margaret Thurmond DePrima. The Institute is privileged to honor the memory of Professor DePrima and his distinguished contribution to mathematics and Caltech, where he served as a faculty member for over forty years, with a lecture each year by an outstanding mathematician. Professor DePrima perceived that there were few or no special talks or seminars designed for undergraduates; he and Margaret DePrima intended that this lecture series would fill that need. 
