关于算术级数的若干著名课题

We have studied several active topics in combinatorial number theory. By means of covering systems we give a residue class.(consisting of odd numbers) containing no sums or differences of two prime powers; we also show that 22^n –1 with n>3 cannot be the sum of two powers of 2 and a prime power. We investigate related algebraic structures of periodic arithmetical maps and study an extremal.problem on covers of groups. We also obtain some deep results on lower bounds for various restricted sumsets in a field. We use recurrent sequences to express the sum ∑k≡r(mod m) C(n,k), and also give vast generalizations of some classical congruences on Bernoulli numbers. Some important advances on Dedekind sums are also made. 15 of our.24 published papers, appeared in famous international mathematical journals and were indexed in SCI.

由算术级数构成的整数集的覆盖，经Erdos提出后受到国际数论界广泛关注，我们将揭示覆窍涤氲ノ环质跋咝孕偷纳钊肓担φ谥腃rittenden-Vanden Eynden 猜想与Erdos问题上有所突破还将应用覆盖研究不能表成两个素数幂和与差的整数等。1998年获Fields蠼钡腉owers的工作涉及van der Waerden定理、Szemeredi定理与子集和问题，我们将致力谟泄厣舷陆