Blum axioms: Difference between revisions
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{{Infobox scientist | |||
|name = Daniel Goldston | |||
|image = Daniel Goldston.jpg | |||
|image_size = | |||
|caption = | |||
|birth_date = {{birth date and age|1954|1|4}} | |||
|birth_place = [[Oakland, California]] | |||
|death_date = | |||
|death_place = | |||
|residence = | |||
|citizenship = | |||
|nationality = [[United States|American]] | |||
|ethnicity = | |||
|fields = [[Mathematics]] | |||
|workplaces = [[San Jose State University]] | |||
|alma_mater = [[University of California at Berkeley|UC Berkeley]] | |||
|doctoral_advisor = | |||
|academic_advisors = | |||
|doctoral_students = | |||
|notable_students = | |||
|known_for = | |||
|influences = | |||
|influenced = | |||
|awards = | |||
|religion = | |||
|signature = <!--(filename only)--> | |||
|footnotes = | |||
}} | |||
'''Daniel Alan Goldston''' (born January 4, 1954 in [[Oakland, California]]) is an [[United States|American]] [[mathematician]] who specializes in [[number theory]]. He is currently a professor of mathematics at [[San Jose State University]]. | |||
Goldston is best known for the following result that he, [[János Pintz]], and [[Cem Yıldırım]] proved in 2005:<ref>http://arxiv.org/abs/math/0508185</ref> | |||
:<math>\liminf_{n\to\infty}\frac{p_{n+1}-p_n}{\log p_n}=0</math> | |||
where <math>p_n\ </math> denotes the nth [[prime number]]. In other words, for every <math>c>0\ </math>, there exist infinitely many pairs of consecutive primes <math>p_n\ </math> and <math>p_{n+1}\ </math> which are closer to each other than the average distance between consecutive primes by a factor of <math>c\ </math>, i.e., <math>p_{n+1}-p_n<c\log p_n\ </math>. | |||
This result was originally reported in 2003 by Dan Goldston and Cem Yıldırım but was later retracted.<ref>http://aimath.org/primegaps/</ref><ref>http://www.aimath.org/primegaps/residueerror/</ref> 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|twin prime conjecture]]. | |||
==See also== | |||
*[[Landau's problems]] | |||
==References== | |||
{{Reflist}} | |||
==External links== | |||
*[http://www.math.sjsu.edu/~goldston/ Dan Goldston's Homepage] | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Goldston, Daniel | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = American mathematician | |||
| DATE OF BIRTH = January 4, 1954 | |||
| PLACE OF BIRTH = [[Oakland, California]] | |||
| DATE OF DEATH = | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Goldston, Daniel}} | |||
[[Category:American mathematicians]] | |||
[[Category:University of California, Berkeley alumni]] | |||
[[Category:San Jose State University faculty]] | |||
[[Category:20th-century mathematicians]] | |||
[[Category:21st-century mathematicians]] | |||
[[Category:Number theorists]] | |||
[[Category:1954 births]] | |||
[[Category:Living people]] | |||
Latest revision as of 17:08, 24 January 2014
Template:Infobox scientist Daniel Alan Goldston (born January 4, 1954 in Oakland, California) is an American mathematician who specializes in number theory. He is currently a professor of mathematics at San Jose State University.
Goldston is best known for the following result that he, János Pintz, and Cem Yıldırım proved in 2005:[1]
where denotes the nth prime number. In other words, for every , there exist infinitely many pairs of consecutive primes and which are closer to each other than the average distance between consecutive primes by a factor of , i.e., .
This result was originally reported in 2003 by Dan Goldston and Cem Yıldırım but was later retracted.[2][3] 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.
See also
References
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