Imperiali quota: Difference between revisions
en>Nlsanand mNo edit summary |
en>Neodymium-142 |
||
| Line 1: | Line 1: | ||
'''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 16:27, 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
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
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