Initial day: July 31, 2001 Last modified: Jan. 29, 2012
visits since April 10, 2002
Number Theory (especially Combinatorial Number Theory),
Combinatorics, Group Theory, Mathematical Logic.
Editor-in-Chief of Journal of Combinatorics and Number Theory, 2009--.
You may submit your paper by sending the pdf file to firstname.lastname@example.org
or to one of the two managing editors Florian Luca and Jiang Zeng. (A sample tex file)
Editorial Board Member of International Journal of Number Theory, 2009--.
Reviewer for Zentralblatt Math., 2007--.
Reviewer for Mathematical Reviews, 1992--.
Member of the American Mathematical Society, 1993--.
Referee for Proc. Amer. Math. Soc., Acta Arith., J. Number Theory, J. Combin. Theory Ser. A, European J. Combin.,
Finite Fields Appl., Adv. in Appl. Math., Discrete Math., Discrete Appl. Math., Ramanujan J., SIAM Review etc.
School Education and Employment History
1980.9--1983.7 The High Middle School Attached to Nanjing Normal Univ.
1983.9--1992.6 Department of Mathematics, Nanjing University
(Undergraduate--Ph. D. Candidate; B. Sc. 1987, Ph. D. 1992)
1992.7-- Teacher in Department of Mathematics, Nanjing University
1994.4--1998.3 Associate Professor in Math.
1998.4-- Full Professor in Math.
1999.11- Supervisor of Ph. D. students
My 100 Open Conjectures on Congruences
My 170 Conjectural Series for Powers of π and Other Constants (Announcements: 1, 2, 3, 4, 5, 6)
Let C(n,k) denote the binomial coefficient n!/(k!(n-k)!) and let Tn(b,c) denote the coefficient of xn in (x2+bx+c)n. Then
∑k ≥ 0 (126k+31)Tk(22,212)3/(-80)3k = 880*sqrt(5)/(21π),
∑k ≥ 0 (221k+28)C(2k,k)Tk(6,2)2/450k = 2700/(7π),
∑k ≥ 0(450296k+53323)C(2k,k)Tk(171,-171)2 /(-5177196)k = 113535*sqrt(7)/(2π).
See all the 58 such conjectural series for 1/π.
∑k>0(10k-3)8k /(k3C(2k,k)2C(3k,k)) = π2/2,
∑k>0(35k-8)81k /(k3C(2k,k)2C(4k,2k)) = 12π2.
∑k>0(28k2-18k+3)(-64)k /(k5C(2k,k)4C(3k,k)) = -14∑n>01/n3.
∑n ≥ 0(28n+5)24-2n C(2n,n)∑k ≥ 05k C(2k,k)2C(2(n-k),n-k)2/C(n,k) = 9(sqrt(2)+2)/π.
∑n ≥ 0(18n2+7n+1)(-128)-n ∑k ≥ 0C(-1/4,k)2C(-3/4,n-k)2 = 4*sqrt(2)/π2.
∑n ≥ 0(40n2+26n+5)(-256)-n ∑k ≥ 0C(n,k)2C(2k,k)C(2(n-k),n-k) = 24/π2.
My Conjecture on Sums of Primes and Triangular Numbers
Each natural number not equal to 216 can be written in the form p+Tx , where p is 0 or a prime, and Tx=x(x+1)/2 is a triangular number. [This has been verified up to 1,000,000,000,000.] In general, for any a,b=0,1,2,... and odd integer r, all sufficiently large integers can be written in the form 2ap +Tx , where p is either zero or a prime congruent to r modulo 2b.
My Conjecture on Sums of Polygonal Numbers
For each integer m>2, any natural number n can be expressed as pm+1(x1) + pm+2(x2) + pm+3(x3) + r with x1,x2,x3 nonnegative integers and r among 0,...,m-3, where pk(x)=(k-2)x(x-1)/2+x (x=0,1,2,...) are k-gonal numbers. In particular, every natural number is the sum of a square, a pentagonal number and a hexagonal number. [For m=3, m=4,...,10, and m=11,...,40, this has been verified for n up to 30,000,000, 500,000 and 100,000 respectively.]
My Conjecture on Sums of Primes and Fibonacci Numbers
Any integer n>4 can be represented as the sum of an odd prime and two or three positive Fibonacci numbers. [This has been verified up to 100,000,000,000,000.]
My Conjecture on Disjoint Cosets
Let a1G1 , ..., akGk (k>1) be finitely many pairwise disjoint left cosets in a group G with all the indices [G:Gi] finite. Then, for some distinct i and j the greatest common divisor of [G:Gi] and [G:Gj] is at least k.
My Conjecture on Covers of Groups
Let a1G1 , ..., akGk be finitely many left cosets in a group G which cover all the elements of G at least m>0 times with ajGj irredundant. Then k is at least m+f([G:Gj]), where f(1)=0 and f(p1 ... pr) =(p1-1) + ... +(pr-1) for any primes p1 , ..., pr .
My Conjecture on Linear Extension of the Erdos-Heilbronn Conjecture
Redmond-Sun Conjecture (in PlanetMath.)
|Papers Indexed in SCI or SCI-E||Papers Listed by Field|
|Recent Publications (2006-)||Preprints on arXiv|
|Publications during 2000-2005||Publications during 1987-1999|
|Research Grants||Awards and Honours|
|Academic Visits||Courses Taught and Ph.D Students|
|Notes on Some Conjectures of Z. W. Sun||Introduction to Sun's Papers on Covers|
|Books and Papers Citing Sun's Work||Webpages of Wall-Sun-Sun Prime [1, 2, 3]|
|Covers, Sumsets and Zero-sums||Link to the useful Number Theory Web|
|Mixed Sums of Primes and Other Terms||Articles on arXiv: Combinatorics, Number Theory|
Invited Lectures in Mathematics|
The copyright of each published or accepted paper is held by the corresponding publisher.