题目: Primes in short intervals

报告人: 孙宇辰，布里斯托大学

时间: 10月22日（周二）下午4:00

地点: 五教5101

摘要: Let $\pi(x)$ denote the number of primes up to $x$. The prime number theorem tells us $\pi(x) \sim \frac{x}{\log x}$. In 1972, Huxley obtains an asymptotic formula for primes in short intervals, namely, $\pi(x+h)-\p(x) \sim \frac{h}{\log x}$ for all sufficiently large $x$ and $x^{7/12+ \epsilon}<h \leq x$. Recently, Maynard and Guth improved this result by showing that the asymptotic formula holds for shorter intervals---$x^{17/30+ \epsilon}<h \leq x$. In this talk, we will introduce Maynard-Guth's methods and main results--large value estimates for Dirichlet polynomials.