Sun Zhiwei

Sun Zhiwei (Chinese: 孙智伟; pinyin: Sūn Zhìwěi; Wade–Giles: Sun Chih-wei, born October 16, 1965) is a Chinese mathematician, working primarily in number theory, combinatorics, and group theory. He is a professor at Nanjing University.

Biography

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 ${\displaystyle \pi }$.[5]

In 2013, he published a paper [6] containing many conjectures on primes, one of which states that for any positive integer ${\displaystyle m}$ there are consecutive primes ${\displaystyle p_{k},\ldots ,p_{n}\ (k<n)}$ not exceeding ${\displaystyle 2m+2.2{\sqrt {m}}}$ such that ${\displaystyle m=p_{n}-p_{n-1}+...+(-1)^{n-k}p_{k}}$, where ${\displaystyle p_{j}}$ denotes the ${\displaystyle j}$-th prime.

In the paper,[7] he refined Lagrange's four-square theorem in various ways and posed many related conjectures one of which is Sun's 1-3-5 conjecture.[8]

He is the Editor-in-Chief of the Journal of Combinatorics and Number Theory.

See also

• Redmond–Sun conjecture
• Sun's curious identity

Notes

1. Unification of zero-sum problems, subset sums and covers of ${\displaystyle \mathbb {Z} }$
2. Mixed sums of squares and triangular numbers (III)
3. On universal sums of polygonal numbers
4. Open conjectures on congruences
5. List of conjectural series for powers of ${\displaystyle \pi }$ and other constants
6. On functions taking only prime values, J. Number Theory 133(2013), 2794-2812
7. Refining Lagrange's four-square theorem, J. Number Theory 175(2017), 167-190
8. http://oeis.org/A271518

External links

• Zhi-Wei Sun's homepage