学术报告（三场）

 

1. 报告人: 吴杰（Institut Elie Cartan Nancy (IECN) & Universite Henri Poincare (Nancy 1), France）

题目: On the density of primes whose shift has large prime factors

摘要: As usual, denote by $P^+(n)$ the largest prime factor of the integer $n>1$ with the convention $P^+(1)=1$. For  $0< \theta<1$, define $$t_{\theta}(x):="|\{p\leq" x: p^+(p-1)>p^{\theta}\}|.$$ 

In this talk, we shall present a new lower bound for $T_{\theta}(x)$, which improves some recent results of Luca- Menares-Madariaga (2015) and Feng Juan Chen-Yong Gao Chen (2016). As a corollary, we disprove a conjecture of Feng Juan  Chen-Yong Gao Chen about the size of T (x). This is a joint work with Bin Feng. 

 

2. 报告人: 郗平（西安交通大学）

题目: Sign changes of Kloosterman sums

摘要: It was conjectured by Nicholas Katz that $S(1,1;p)/\sqrt{p}$ becomes equidistributed with respect to the Sato-Tate  measure as $p$ runs over primes, from which it follows that $S(1,1;p)$ must change sign infinitely often. By introducing  an elaborate weight in Selberg sieves and invoking certain equidistributions of Kloosterman sums from $\ell$-adic  cohomology, we give an affirmative answer to the problem on sign changes if relaxing the moduli to squarefree numbers  with at most 7 prime factors. 

 

3. 报告人: 刘奎（青岛大学）

题目: Bilinear forms with exponential sums with binomials

摘要: We obtain several estimates for bilinear form with exponential sums with binomials $mx^k+nx^l$. 

 

 

时间：12月23日（周五），8:30-11:30

 

地点：数学院304报告厅

 

 

热烈欢迎各位老师和同学参加！