Enrico Bombieri

**Enrico Bombieri**
	Enrico Bombieri
	; Enrico Bombieri
Born	November 26, 1940 (age 68);
Nationality	Italian
Fields	mathematics
Institutions	Institute of Advanced Study
Alma mater	Trinity College, Cambridge
Doctoral advisor	Harold Davenport
Known for	Large sieve method in analytic number theory; Bombieri-Lang conjecture; Bombieri norm; Bombieri–Vinogradov theorem; "Heights" in Diophantine geometry; Siegel's lemma for bases (Bombieri–Vaaler); Partial differential equations
Notable awards	1974, Fields medal

Enrico Bombieri (born November 26, 1940) is an Italian mathematician, born in Milan. He is now at the Institute for Advanced Study. He is known for work in number theory, algebraic geometry, and mathematical analysis. He was awarded a Fields Medal in 1974.

The Bombieri–Vinogradov theorem is one of the major applications of the large sieve method. It improves Dirichlet's theorem on prime numbers in arithmetic progressions, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case. This result can sometimes substitute for the still-unproved generalized Riemann hypothesis.

In 1976, he developed the technique known as the asymptotic sieve.^[1]

Bombieri is also known for his pro bono service to the mathematics profession, for example, serving on external review boards and for peer-reviewing extraodinarily complicated manuscripts (like papers of John Nash on embedding Riemann manifolds and of Per Enflo solving the invariant subspace problem for Banach spaces).

Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.

[edit] See also

^ E. Bombieri, "The asymptotic sieve", Mem. Acad. Naz. dei XL, 1/2 (1976) 243–269.

Bombieri, E.; Mueller, J. (1983). "On effective measures of irrationality for ${\scriptscriptstyle\sqrt[r]{a/b}}$ and related numbers". Journal für die reine und angewandte Mathematik 342: 173-196.
Bombieri, E.; Vaaler, J. (Feb 1983). "On Siegel's lemma". Inventiones Mathematicae 73 (1): 11–32. doi:10.1007/BF01393823. http://www.springerlink.com/content/k55042224131lp42.
E. Bombieri, Le Grand Crible dans la Théorie Analytique des Nombres (Seconde Édition). Astérisque 18, Paris 1987.
B. Beauzamy, E. Bombieri, P. Enflo and H. L. Montgomery. "Product of polynomials in many variables", Journal of Number Theory, pages 219--245, 1990.
Enrico Bombieri and Walter Gubler (2006). Heights in Diophantine Geometry. Cambridge U. P..

Enrico Bombieri
Enrico Bombieri
Born	November 26, 1940 (1940-11-26) (age 68)
Nationality	Italian
Fields	mathematics
Institutions	Institute of Advanced Study
Alma mater	Trinity College, Cambridge
Doctoral advisor	Harold Davenport
Known for	Large sieve method in analytic number theory Bombieri-Lang conjecture Bombieri norm Bombieri–Vinogradov theorem "Heights" in Diophantine geometry Siegel's lemma for bases (Bombieri–Vaaler) Partial differential equations
Notable awards	1974, Fields medal