Henri Cohen

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Henri Cohen in Oberwolfach 2007

Henri Cohen (born June 8, 1947 ) is a French mathematician who deals with algorithmic number theory.

Cohen studied from 1966 to 1970 at the École normal supérieure , among others with Jean-Louis Verdier and Jean-Pierre Serre . In 1976 he completed his habilitation (Doctorat d'Etat) at the University of Bordeaux with Jacques Martinet (Formes modulaires à une ou deux variables). In 1978 he became a professor at the University of Grenoble and from 1981 was professor at the University of Bordeaux , where he built a French school of algorithmic number theory. He is now Professor Emeritus there.

Cohen was concerned with computer applications in number theory since the late 1960s. In 1981 he improved and implemented with Hendrik Lenstra the APRCL primality test (after the initial letters of the developers) by Robert Rumely , Carl Pomerance and Leonard Adleman from 1980, an extension of the Fermat's primality test , which is still widely used today and was the first test that was also efficiently applicable to the prime numbers of a hundred or more digits used in public key cryptography ( RSA ) (1000 or 2000 digits are used today).

Cohen also developed algorithms in algebraic number theory, for example for the determination of class fields , and in the 1990s he partially collaborated with Francisco Diaz y Diaz and Michel Olivier (for example on quaternary number fields ). With Lenstra in 1982 he made heuristic conjectures about the structure of the class groups of quadratic number fields , which became an important unsolved problem in algebraic number theory. Heuristics of class groups of higher number fields he investigated with his teacher in Bordeaux Jacques Martinet (Cohen-Martinet heuristics). Cohen is known not least for some textbooks on algorithmic number theory. Around 1985 he developed the free computer algebra software package PARI / GP, written in C , for number theoretic applications , today maintained by Karim Belabas from the University of Toulouse. It is one of the most widely used computer algebra systems in number theory.

In 2000 he received the FL Bauer Prize from the Technical University of Munich . In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (Constructing and counting number fields).

Fonts

  • A course in computational algebraic number theory. Springer, Graduate Texts in Mathematics Vol. 138, 1st edition 1993, 4th edition 2000, ISBN 0-387-55640-0 .
  • Advanced topics in computational number theory. Graduate Texts in Mathematics, Vol. 193, Springer, 2000, ISBN 0-387-98727-4 .
  • Number Theory. Springer, Graduate Texts in Mathematics, Vol. 239/240, 2 volumes (Vol. 1 Tools and Diophantine Equations, ISBN 978-0-387-49922-2 , Vol. 2 Analytic and modern tools, ISBN 978-0-387- 49893-5 ), 2007.
  • Editor with Gerhard Frey : Handbook of elliptic and hyperelliptic curve cryptography. Chapman and Hall, 2006 (authors Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren).

Web links

References

  1. ^ Henri Cohen in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ The Fermat congruence is tested in some higher number fields, especially circular fields.
  3. ^ Henri Cohen, Hendrik Lenstra: Primality testing and Jacobi sums. Mathematics of Computation, Vol. 42, 1984, pp. 297-330; Henri Cohen, Arjen Lenstra : Implementation of a new primality test, Math. Computation, Vol. 48, 1987, pp. 103-121.
  4. ^ Henri Cohen, Hendrik Lenstra: Heuristics on class groups of number fields, in: Number Theory- Noordwijkerhout 1983, Lecture Notes in Mathematics, Vol. 1068, 1984, p. 33, for example Klueners, Fouvry Cohen-Lenstra heuristics of quadratic number fields ( Memento of the original from June 25, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 203 kB); Henri Cohen: A course in computational algebraic number theory. Springer 1996, p. 296. @1@ 2Template: Webachiv / IABot / www.math.uni-duesseldorf.de
  5. ^ Henri Cohen, Jacques Martinet: Class groups of number fields - numerical heuristics. Math. Computation, Vol. 48, 1987, p. 123, Heuristics on class groups: some good primes are not too good, Math. Computation, Vol. 63, 1994, p. 329.
  6. ↑ But the program had a forerunner in the interpreter Isabelle, written by Cohen and François Dress in 1979 .
  7. ↑ GP is the command line interface
personal data
SURNAME Cohen, Henri
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH June 8, 1947