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Cem Yıldırım

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Citizenship
  
Republic of Turkey

Institutions
  
Bogazici University

Role
  
Mathematician

Fields
  
Mathematics

Doctoral advisor
  
Nationality
  
Turkish

Name
  
Cem Yildirim

Notable awards
  
Cem Yildirim wwwmathbounedutrinstructorsyildirimyildirimjpg
Born
  
June 8, 1961 (age 63) (
1961-06-08
)

Alma mater
  

ICM2014 VideoSeries IL3.4: Dan Goldston, János Pintz, Cem Yildirim on Aug15Fri


Cem Yalçın Yıldırım (born 8 July 1961) is a Turkish mathematician who specializes in number theory. He obtained his B.Sc from Middle East Technical University in Ankara, Turkey and his PhD from the University of Toronto in 1990. His advisor was John Friedlander. He is currently a faculty member at Boğaziçi University in Istanbul, Turkey.

Cem Yıldırım httpswwwmuhendisbeyinlernetwpcontentupload

In 2005(), with Dan Goldston and János Pintz, he proved, that for any positive number ε there exist primes p and p′ such that the difference between p and p′ is smaller than ε log p.

Formally;

lim inf n p n + 1 p n log p n = 0

where pn denotes the nth prime number. In other words, for every c > 0, there exist infinitely many pairs of consecutive primes pn and pn+1 which are closer to each other than the average distance between consecutive primes by a factor of c, i.e., pn+1 − pn < c log pn.

This result was originally reported in 2003 by Dan Goldston and Cem Yıldırım but was later retracted. Then Janos Pintz joined the team and they completed the proof in 2005.

In fact, if they assume the Elliott–Halberstam conjecture, then they can also show that primes within 16 of each other occur infinitely often, which is related to the twin prime conjecture.

References

Cem Yıldırım Wikipedia


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