算术数列中的素数分布、素数的表示、华林问题以及加乘问题均是解析数论中的重要问题。本项目将系统地研究解析数论中的一些堆垒问题和加乘问题。对于堆垒问题，本项目主要致力于华林问题中G(k)的上界估计，Linnik-Goldbach问题以及Hardy-Littlewood数问题。对于算术数列中的素数分布，本项目致力于研究算术数列中素数分布有相应渐进公式的成立范围，特别是在几乎所有的意义下。另一个问题就是关于算术数列中的相邻素数和殆素数的小差问题。对于加乘问题，本项目致力于研究Erdos猜想，期望在实数域以及有限域上对该猜想取得重要进展。

The distribution of primes in arithmetic progressions,the representation of primes,Waring's problems and sum-product problems are all the important problems in analytic number theory. In this project, we will systematically study some additive problems and sum-product problems in analytic number theory.For additive problems, this project focus on the upper bound of G(k) in Waring's problems,the Linnik-Goldbach problems and Hardy-Littlewood numbers.For prime numbers in arithmetic progression,this project studies the distribution of primes in arithmetic progressions and wish to enlarge the range of module in the meaning of almost sense. Another problem is the small gap between consecutive primes and almost primes in arithmetic progressions. For sum-product problems, this project focus on the Erdos conjecture and wish to get improvement for this conjecture in real fields and finite fields.