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 .[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.

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

Notes

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.