# Henri Cohen (number theorist)

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

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

Cohen was concerned since the late 1960s with computer applications in number theory. He improved and implemented in 1981 with Hendrik Lenstra the APRCL primality test ( after the initials of the developer ) by Robert Rumely, Carl Pomerance, and Leonard Adleman in 1980, an extension of Fermat's primality test, which is used a lot today and the first test was the also used to in the public-key cryptography ( RSA) primes of a hundred or more points (to be used in 1000 and 2000 points today ) was efficiently applicable.

Cohen also developed in algebraic number theory algorithms, for example for the determination of class bodies, where he in the 1990s partly worked with Francisco Diaz y Diaz, and Michel Olivier (eg via quaternary number field ). With Lenstra he set up in 1982 heuristic assumptions about the structure of the class groups of quadratic number fields that have an important unsolved problem in algebraic number theory. Heuristics of class groups of higher number field he also studied with his teacher in Bordeaux Jacques Martinet ( Cohen- Martinet heuristics ). Cohen is known, not least by some textbooks on algorithmic number theory. For number-theoretic applications, he developed around 1985, the free, written in C computer algebra software package PARI / GP today by Karim Belabas of the University of Toulouse. It is one of the most widely used computer algebra systems in number theory.

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

## Writings

- A course in computational algebraic number theory, Springer, Graduate Texts in Mathematics Bd.138, 1st edition 1993, 4th edition 2000, ISBN 0-387-55640-0
- Advanced topics in computational number theory, Graduate Texts in Mathematics, Bd.193, Springer, 2000, ISBN 0-387-98727-4
- Number Theory, Springer Verlag, Graduate Texts in Mathematics Bd.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
- Publisher Gerhard Frey: Handbook of elliptic and hyperelliptic curve cryptography, Chapman and Hall, 2006 ( authors Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren )