number theory;
prime sums;
elliptic theta functions;
Euler-totient constant;
Mobius function;
Mobius inversion theorem;
Riemann zeta function;
Euler's prime number theorem;
D O I:
10.1134/S0001434611070029
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
We study sums of primes by means of a generalization of Euler's prime number theorem and use the values of the Riemann zeta function for the approximation. We also give the truncation error of these approximations.