Harold Stark

Harold Mead Stark ( born August 6, 1939 in Los Angeles ) is an American number theorist.

Life

Stark was founded in 1964 his doctorate at the University of California, Berkeley with Derrick Lehmer with the dissertation On the Tenth Complex Quadratic Field with Class Number One. 1970/71 he was in Princeton, New Jersey at the Institute for Advanced Study. After he was a professor at the Massachusetts Institute of Technology (MIT), he is currently at the University of California, San Diego.

Stark is known for the solution of the Gaussian class number problem, the proof that there are exactly nine imaginary quadratic fields with class number 1. Already in the 1930s was known by Deuring, Heilbronn and Linfoot, that there are in addition to the already suspected by Carl Friedrich Gauss nine bodies at most another with class number 1. Stark proved his theorem by methods of analytic number theory, he examined the behavior of the functions of binary quadratic forms on the site. Later it turned out that a previous proof of the theorem of Stark by Kurt Heegner essentially was also correct. Alan Baker was with completely different methods around the same time (1966 ) as Stark also a proof of this theorem.

From him the Stark conjectures, which provide a link between analytic and algebraic variables for finite Galois extensions of algebraic number fields originate. More specifically, the first non-zero coefficient of the Taylor expansion function is applied to the Artin (a kind Dirichlet function, which is formed with the help of diagrams the Galois group ) at the location in accordance with the assumptions by the regulator of the high - units. Stark proved this conjecture for functions of abelian extensions over the rational numbers and imaginary quadratic number fields. The Stark conjectures provide ( through provision of these units) algorithms for partial solutions to Hilbert's 12th problem of explicit construction of class bodies and are a current area of ​​research in algebraic number theory.

In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (Class number problems in quadratic fields ). His doctoral include Ram Murty M., Andrew Odlyzko, Kenneth Rosen, Jeffrey Lagarias, Jeffrey Hoffstein.

Writings

  • Class -number problems in quadratic fields. International Congress of Mathematicians 1970, p 511
  • Class numbers of complex quadratic fields. Lecture Notes in Mathematics, Vol 320. 1973, pp. 153-174.
  • Class fields and modular forms of weight one. In: Modular Functions of one variable. Lectures Notes in Mathematics, Vol 601. 1976, p 277
  • An Introduction to Number Theory. MIT Press, 1978, ISBN 0-262-69060-8.
  • Galois theory, algebraic number theory, and zeta functions. In Michel Waldschmidt, Claude Itzykson, Jean -Marc Luck, Pierre Moussa (Editor ): Number Theory and Physics, Les Houches 1989, Springer, 1992
Harold Rainsford Stark Princeton (New Jersey) Alan Baker (mathematician) M. Ram Murty John Tate Mathematics Genealogy Project Inventiones Mathematicae Carl Ludwig Siegel
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