Dorian M. Goldfeld

Dorian Morris Goldfeld ( born January 21, 1947 in Marburg) is an American mathematician who deals with number theory.

Career

Goldfeld his degree (BS ) in 1967 at Columbia University in New York and received his doctorate in 1969 at Patrick Gallagher with Some methods of averaging in analytical number theory, in which he an averaged version of Artin 's conjecture ( on the distribution of primes p for a given number a is a primitive root mod p ) showed ( Mathematika Vol 15, 1968). 1969 and 1971 he worked as a Miller Fellow at Berkeley, 1971/2 at the Hebrew University in Jerusalem and then 1971/2 at the University of Tel Aviv, 1973/4 at the Institute for Advanced Study at Princeton, 1974-76 in Italy, 1976 to 1982 at MIT ( 1973-1974 ) from 1983 to 1985 at the University of Texas at Austin and from 1983 to 1985 at Harvard. Since 1985 he is a professor at Columbia University.

In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( Kloosterman zeta functions for GL (n, Z)). He is a Fellow of the American Mathematical Society.

Field of activity

Gold Field is known mainly for his work on the class number problem imaginary quadratic number field. Gauss had 9 class field lists the class number 1, and it was proved in the 1960s by Harold Stark, that this list is complete ( an older proof of Kurt Heegner was shortly thereafter also rehabilitated and given an alternative proof by Alan Baker). Goldfeld showed in a paper from the year 1976 ( Ann. Sc. Standard. Sup Pisa Vol 3, No. 4) a way to take the general case of arbitrary number of classes in attack by a connection to properties of L-functions elliptic curves created. Benedict Gross and Don Zagier completed in the 1980s, this method of effective determination of the class body with a given class number.

Next he worked example on the abc conjecture ( a generalization of Fermat 's conjecture ), size estimates of the Tate - Shafarevich groups (important in conjunction with the detailed version of the conjecture of Birch and Swinnerton - Dyer ), modular forms for the general linear group GL ( n ) ( in related to the Langlands program) and examined multiple Dirichlet series.

Goldfeld also dealt with cryptography. He reasoned with Iris and Michael Anshel encryption methods based on the braid group. He is also co-founder of SecureRF that offers fast authentication method for RFID.

Gold field in 1987 received the Cole prize in number theory, was 1977-1979 Sloan Fellow and received the 1985 Vaughn price.

Among his students Jeffrey Hoffstein, M. Ram Murty, Ilan Vardi.