Abstract:
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.
Keywords:number theory, prime sums, elliptic theta functions, Euler-totient constant, Möbius function, Möbius inversion theorem, Riemann zeta function, Euler's prime number theorem.
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