Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics (ICTP).[2]
Background
Zagier was born in Heidelberg, West Germany. His mother was a psychiatrist, and his father was the dean of instruction at the American College of Switzerland. His father held five different citizenships, and he spent his youth living in many different countries. After finishing high school (at age 13) and attending Winchester College for a year, he studied for three years at MIT, completing his bachelor's and master's degrees and being named a Putnam Fellow in 1967 at the age of 16.[3] He then wrote a doctoral dissertation on characteristic classes under Friedrich Hirzebruch at Bonn, receiving his PhD at 20. He received his Habilitation at the age of 23, and was named professor at the age of 24.[4]
Work
Zagier collaborated with Hirzebruch in work on Hilbert modular surfaces. Hirzebruch and Zagier coauthored Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus,[5] where they proved that intersection numbers of algebraic cycles on a Hilbert modular surface occur as Fourier coefficients of a modular form. Stephen Kudla, John Millson and others generalized this result to intersection numbers of algebraic cycles on arithmetic quotients of symmetric spaces.[6]
Zagier found a formula for the value of the Dedekind zeta function of an arbitrary number field at s = 2 in terms of the dilogarithm function, by studying arithmetic hyperbolic 3-manifolds.[9] He later formulated a general conjecture giving formulas for special values of Dedekind zeta functions in terms of polylogarithm functions.[10]
Zagier, D. (1990), "A One-Sentence Proof That Every Prime p ≡ 1 (mod 4) Is a Sum of Two Squares", The American Mathematical Monthly, 97 (2), Mathematical Association of America: 144, doi:10.2307/2323918, JSTOR2323918. The First 50 Million Prime Numbers." Math. Intel. 0, 221–224, 1977.
Zagier, Don (1991). "The Birch-Swinnerton-Dyer Conjecture from a Naive Point of View". Arithmetic Algebraic Geometry. Boston, MA: Birkhäuser Boston. pp. 377–389. doi:10.1007/978-1-4612-0457-2_18. ISBN978-1-4612-6769-0.
Zagier, Don (1991). "Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields". Arithmetic Algebraic Geometry. Boston, MA: Birkhäuser Boston. pp. 391–430. doi:10.1007/978-1-4612-0457-2_19. ISBN978-1-4612-6769-0.