J W Sander - On some over primes

hrj:129 - Hardy-Ramanujan Journal, January 1, 1994, Volume 17 - https://doi.org/10.46298/hrj.1994.129
On some over primes

Authors: J W Sander

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.

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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