Editing Enrico Bombieri (section)

==Research==
The [[Bombieri–Vinogradov theorem]] is one of the major applications of the [[large sieve method]]. It improves [[Dirichlet's theorem on arithmetic progressions|Dirichlet's theorem]] on prime numbers in [[arithmetic progression]]s, 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 1969, Bombieri, [[Ennio De Giorgi|De Giorgi]], and [[Enrico Giusti|Giusti]] solved [[Bernstein's problem]] on minimal surfaces in dimensions above eight.<ref>{{Citation | last1=Bombieri | first1=Enrico | last2=De Giorgi | first2=Ennio | last3=Giusti | first3=Enrico | title=Minimal cones and the Bernstein problem | doi=10.1007/BF01404309 | mr=0250205 | year=1969 | journal=[[Inventiones Mathematicae]] | issn=0020-9910 | volume=7 | issue=3 | pages=243–268| bibcode=1969InMat...7..243B | s2cid=59816096 }}</ref>

In 1976, Bombieri developed the technique known as the "asymptotic sieve".<ref name="asymp-sieve">E. Bombieri, "The asymptotic sieve", ''[[:it:Accademia Nazionale delle Scienze|Mem. Acad. Naz. dei XL]]'', 1/2 (1976) 243–269.</ref> In 1980, he supplied the completion of the proof of the uniqueness of [[Ree group|finite groups of Ree type]] in [[characteristic (algebra)|characteristic]] 3; at the time of its publication, it was one of the missing steps in the [[classification of finite simple groups]].<ref>{{cite journal|author=Bombieri, E.|title=Thompson's problem σ<sup>2</sup>=3. Appendices by A. Odlyzko and D. Hunt|journal=Invent. Math.|volume=58|issue=1|year=1980|pages=77–100|doi=10.1007/bf01402275|s2cid = 122867511}} (This paper completed a line of research initiated by the [[Walter theorem]].)</ref>