2020/06/24 by Victor Volfson, Volfson, Victor
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2006.16759
We will study the asymptotic behavior of summation functions of a natural argument, including the asymptotic behavior of summation functions of a prime argument in the paper. A general formula is obtained for determining the asymptotic behavior of the sums of functions of a prime argument based on the asymptotic law of primes. We will show, that under certain conditions: ∑p ≤ n f(p)= ∑k=2n \frac f(k)log(k)(1+o(1)), where p is a prime number. In the paper, the necessary and sufficient conditions for the fulfillment of this formula are proved.