Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01108738v1

Volume: Volume 17

Published on: January 1, 1994

Submitted on: March 3, 2015

Keywords: prime factors of binomial coefficients,[MATH] Mathematics [math]

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