Sun Zhiwei

Zhi-Wei Sun (Chinese: 孙智伟; pinyin: Sūn Zhìwěi; Wade–Giles: Sun Chihwei, born October 16, 1965) is a Chinese mathematician, working primarily in number theory, combinatorics, and group theory. He is currently a professor at 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 $\pi$.^[5]

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

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 $\mathbb {Z}$
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 $\pi$ and other constants
6. On functions taking only prime values, J. Number Theory 133(2013), 2794-2812

External links

• Zhi-Wei Sun's homepage