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'''Zhi-Wei Sun''' ({{zh|c=孙智伟|p=Sūn Zhìwěi|w='''Sun Chihwei'''}}, born October 16, 1965) is a [[China|Chinese]] [[mathematician]], working primarily on [[number theory]], [[combinatorics]], and [[group theory]]. Currently he works as a professor in [[Nanjing University]]. | |||
Born in [[Huai'an|Huai'an, Jiangsu]], Sun and his twin brother [[Sun Zhihong]] proved a theorem about what are now known as the [[Wall-Sun-Sun prime]]s that guided the search for counterexamples to [[Fermat's last theorem]]. | |||
In 2003, he presented a unified approach to three famous topics of [[Paul Erdős]] in combinatorial number theory: [[covering system]]s, [[restricted sumset]]s, and [[zero-sum problem]]s or EGZ Theorem.<ref>[http://www.ams.org/era/2003-09-07/S1079-6762-03-00111-2/S1079-6762-03-00111-2.pdf Unification of zero-sum problems, subset sums and covers of <math>\Z</math>]</ref> | |||
He used [[q-series]] to prove that any natural number can be represented as a sum of an even [[Square number|square]] and two [[triangular number]]s. He conjectured, and proved with B.-K. Oh, that each positive integer can be represented as a sum of a square, an odd square and a triangular number.<ref>[http://arxiv.org/abs/0804.3750 Mixed sums of squares and triangular numbers (III)]</ref> In 2009, he conjectured that any natural number can be written as the sum of two squares and a [[pentagonal number]], as the sum of a [[triangular number]], an even square and a [[pentagonal number]], and as the sum of a square, a [[pentagonal number]] and a [[hexagonal number]].<ref>[http://arxiv.org/abs/0905.0635 On universal sums of polygonal numbers]</ref> | |||
He also raised many open conjectures on congruences <ref>[http://arxiv.org/abs/0911.5665 Open conjectures on congruences]</ref> | |||
and posed over 100 conjectural series for powers of <math>\pi</math>.<ref>[http://arxiv.org/abs/1102.5649 List of conjectural series for powers of <math>\pi</math> and other constants]</ref> | |||
In 2013 he published a paper <ref>[http://www.sciencedirect.com/science/article/pii/S0022314X13000747 On functions taking only prime values], J. Number Theory 133(2013), 2794-2812</ref> containing many conjectures on primes one of which states that for any positive integer <math>m</math> there are consecutive primes <math>p_k,\ldots,p_n\ (k<n)</math> not exceeding <math>2m+2.2\sqrt{m}</math> such that <math>m=p_n-p_{n-1}+...+(-1)^{n-k}p_k</math>, where <math>p_j</math> denotes the <math>j</math>-th prime. | |||
His [[Erdős number]] is 2. He is the Editor-in-Chief of [https://www.novapublishers.com/catalog/product_info.php?products_id=7065 Journal of Combinatorics and Number Theory]. | |||
==See also== | |||
*[[Redmond–Sun conjecture]] | |||
*[[Sun's curious identity]] | |||
==Notes== | |||
{{reflist}} | |||
==External links== | |||
* [http://math.nju.edu.cn/~zwsun/ Zhi-Wei Sun's homepage] | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Sun, Zhi-Wei | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = Chinese mathematician | |||
| DATE OF BIRTH = October 16, 1965 | |||
| PLACE OF BIRTH = | |||
| DATE OF DEATH = | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Sun, Zhi-Wei}} | |||
[[Category:1965 births]] | |||
[[Category:Living people]] | |||
[[Category:Chinese mathematicians]] | |||
[[Category:20th-century mathematicians]] | |||
[[Category:21st-century mathematicians]] | |||
[[Category:Number theorists]] | |||
[[Category:Combinatorialists]] | |||
[[Category:People's Republic of China science writers]] | |||
[[Category:Writers from Huai'an]] | |||
[[Category:Educators from Jiangsu]] | |||
[[Category:Nanjing University faculty]] | |||
[[Category:Scientists from Jiangsu]] | |||
Revision as of 17:27, 22 August 2013
Zhi-Wei Sun (Template:Zh, born October 16, 1965) is a Chinese mathematician, working primarily on number theory, combinatorics, and group theory. Currently he works as a professor in Nanjing University.
Born in Huai'an, Jiangsu, Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall-Sun-Sun primes that guided the search for counterexamples to Fermat's last theorem.
In 2003, he presented a unified approach to three famous topics of Paul Erdős in combinatorial number theory: covering systems, restricted sumsets, and zero-sum problems or EGZ Theorem.[1]
He used q-series to prove that any natural number can be represented as a sum of an even square and two triangular numbers. He conjectured, and proved with B.-K. Oh, that each positive integer can be represented as a sum of a square, an odd square and a triangular number.[2] In 2009, he conjectured that any natural number can be written as the sum of two squares and a pentagonal number, as the sum of a triangular number, an even square and a pentagonal number, and as the sum of a square, a pentagonal number and a hexagonal number.[3] He also raised many open conjectures on congruences [4] and posed over 100 conjectural series for powers of .[5]
In 2013 he published a paper [6] containing many conjectures on primes one of which states that for any positive integer there are consecutive primes not exceeding such that , where denotes the -th prime.
His Erdős number is 2. He is the Editor-in-Chief of Journal of Combinatorics and Number Theory.
See also
Notes
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External links
- ↑ Unification of zero-sum problems, subset sums and covers of
- ↑ Mixed sums of squares and triangular numbers (III)
- ↑ On universal sums of polygonal numbers
- ↑ Open conjectures on congruences
- ↑ List of conjectural series for powers of and other constants
- ↑ On functions taking only prime values, J. Number Theory 133(2013), 2794-2812
