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The
19th Annual Charles R. DePrima Memorial
Don
Zagier Zeta functions, periods, and Diophantine equations Abstract: In 1734, Euler discovered his famous formula saying that the number 1 + 1/4 + 1/9 + ... (the sum of the reciprocals of the squares of the natural numbers) equals \pi^2/6 . This identity is an example of a formula describing the special value of a "zeta function" (in this case, the "Riemann zeta function") in terms of a "period" (a number expressible as the integral of an algebraic function; in this case, the number \pi). Today many such formulas are known or conjectured, often with surprising connections to other mathematical questions. One of the deepest of these connections is the Birch  SwinnertonDyer conjecture, one of the seven milliondollar Clay Millenium problems, which predicts the solvability of certain Diophantine equations in terms of the values and derivatives of an appropriate zeta function. In the lecture we will try to explain these ideas and some of the related recent research. Dr. Zagier was born in1951. Studies of mathematics and physics, M.I.T. 19661968. D.Phil., Oxford University 1971. Habilitation, University of Bonn 1975. Member, SFB Theoretische Mathematik, University of Bonn 19711984. Professor, University of Bonn since 1976. Chair Professor of Number Theory, University of Maryland 19791990. Professor, Kyushu University (Fukuoka, Japan) 19901991 and 19921993. Professor, University of Utrecht 19902001. Scientific Member, MPI for Mathematics since 1984. Director, MPI for Mathematics since 1995. Professor, Collège de France (Paris) since 2000. Carus Prize 1984. Frank Nelson Cole Prize 1987. Karl Georg Christian von Staudt Prize 2001. 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. 
