# Enrico Bombieri

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Enrico Bombieri (born 26 November 1940 born in Milan, Italy) is a mathematician who has been working at the Institute for Advanced Studies in Princeton, New Jersey. Bombieri research in number theory, algebraic geometry, and mathematical analysis have earned him many international prizes --- a Fields Medal in 1974 and the Balzan Prize in 1980. In 2010 he received the King Faisal International Prize (jointly with Terence Tao).[1]

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".[2]

Bombieri is also known for his pro bono service on behalf of the mathematics profession, e.g. for serving on external review boards and for peer-reviewing extraordinarily complicated manuscripts (like the papers of John Nash on embedding Riemannian manifolds and of Per Enflo on the invariant subspace problem).

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

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### References

• 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.
• 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..