5 citations · 8 across the 8 of their papers we have counts for
8 papers
The restricted sumsets in finite abelian groups
Shanshan Du, Hao Pan
Suppose that and is a non-empty subset of a finite abelian group with . Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1…
The Explicit Formula and Parity for Some Generalized Euler Functions
Shichun Yang, Qunying Liao, Shan Du +1
Based on elementary methods and techniques, the explicit formula for the generalized Euler function is given, and then a sufficient and necessary condition for $…
Vinogradov three prime theorem with Piatetski-Shapiro primes
Yu-Chen Sun, Shanshan Du, Hao Pan
We prove that, for any , every sufficiently large odd number can be represented as the sum of three primes such that $p_i = \lfloo…
On the number of three-term arithmetic progressions in a dense subset of
Shanshan Du, Hao Pan
Let be an odd prime power. Combining the discussion of Varnavides and a recent theorem of Ellenberg and Gijswijt, we show that a subset will contain m…
On the generalized restricted sumsets in abelian groups
Shanshan Du, Hao Pan
Suppose that , and are non-empty subsets of a finite abelian group . Then the generalized restricted sumset $$ A\stackrel{S}+B:=\{a+b:\,a\in A,\ b\in B,\ a-b\not\in S…
A generalization of Frieman's 3k-3 theorem
Shanshan Du, Hao Pan
We prove a generalization of Frieman's theorem for the sumset $$ Σ^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}…
Restricted Sumsets in Finite Nilpotent Groups
Shanshan Du, Hao Pan
Suppose that are two non-empty subsets of the finite nilpotent group . If , then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a\ne…
On a sumset problem for integers
Shan-Shan Du, Hui-Qin Cao, Zhi-Wei Sun
Let be a finite set of integers. We show that if is a prime power or a product of two distinct primes then provided $|A|\…