Jeffrey Lagarias

Jeffrey Clark Lagarias ( born November 16, 1949 in Pittsburgh) is an American mathematician.

Lagarias in 1970 Putnam Fellow (as winner of the competition ) and studied at the Massachusetts Institute of Technology (MIT), where he received his doctorate in 1974 at Harold Stark. From 1975 he was involved in the ATT Bell Laboratories, where he was Distinguished Member of the Technical Staff. Since 1995 he is a consultant (Technology Consultant) at ATT Research Laboratories. He became a professor at the University of Michigan in 2002.

Lagarias worked among other things on number theory, complexity theory, cryptography, mathematical physics, dynamical systems, low dimensional topology ( knot theory ), Linear optimization and discrete geometry ( such as circuit packs, quasicrystals ). He was with Peter Shor in 1992 a counterexample to Keller 's conjecture. He also proved that the following elementary conjecture is equivalent to the Riemann Hypothesis:

It is the sum of the divisor and from the - th harmonic number.

He also worked on the Collatz problem. Lagarias with Gábor Fejes Tóth was the guest editor of the special issue of Discrete & Computational Geometry, which published the proof of the Kepler conjecture. Lagarias has been involved in the review of the proof of Thomas C. Hales and Samuel P. Ferguson, which took place in the form of a one-week workshop in 1999 at the Institute for Advanced Study and summarized the structure of the proof in a paper together, which appeared in Discrete & Computational Geometry, 2002. As of 2003, Lagarias was also actively involved in the problem in peer review of papers by Hales and Ferguson.

He is a Fellow of the American Mathematical Society.

Writings

  • The 3x 1 Problem and its generalizations, American Mathematical Monthly 92, 1985, p 3-23
  • An elementary problem- equivalent to the Riemann hypothesis, American Mathematical Monthly 109, 2002, pp. 534-543.
  • Jeffrey C. Lagarias (ed.): The ultimate challenge: The 3x 1 Problem. Amer. Math Soc., Providence RI 2010, ISBN 0-8218-4940-9.
  • Hilbert spaces of Entire functions and Dirichlet L -functions, in Pierre Cartier, Bernard Julia, Pierre Moussa, Pierre Vanhove (Editor) Frontiers in Number Theory, Geometry and Physics, Volume 1, Springer Verlag, 2006
  • Euler's constant: Euler 's work and modern Developments, Bulletin of the AMS, Volume 50, 2013, pp. 527-628
  • As Publisher: The Kepler conjecture. The Hales -Ferguson proof, Springer Verlag 2011 ( with Thomas C. Hales, Samuel P. Ferguson, the introductory chapters are of Lagarias )
  • Published by Michael J. Todd: Mathematical Developments Arising from linear programming, Contemporary Mathematics 114, American Mathematical Society 1990
  • Point lattices, Handbook of Combinatorics, Elsevier 1995, pp. 919-966
  • Bounds for local density of sphere packings and the Kepler conjecture, Discrete & Computational Geometry, Volume 27, 2002, 165-193 (also reprinted in the book published by him about the Kepler conjecture )
Ott-Heinrich Keller Thomas Callister Hales Integrated Authority File
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