Volume 17

1. Estimate of sums of Dirichlet series

Shituo, Lou ; Qi, Yao.
This paper discusses the problem of primes in short intervals using certain analytical considerations involving mean value estimates for products of Dirichlet polynomials and series.

2. On some over primes

Sander, J W.
It will be shown that, for any $\delta > 0$, \[ {\sum_{p\leq n}}^* \; \frac{\log p}{p} = \frac{1}{2} \log n + O\Big((\log n)^{\frac{5}{6}+\delta}\Big), \] where (*) restricts the summation to those primes $p$, which satisfy $n = kp+r$ for some integers $k$ and $r$, $p/2 < r < p$. This result is connected with questions concerning prime divisors of binomial coefficients.