The paper attempts to prove an equivalence between the error in a smooth weighted prime number theorem and zero-free regions for the Riemann zeta function, but critical proof errors undermine the result.
Goldbach Representations with several primes
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We study an asymptotic formula for average orders of Goldbach representations of an integer as the sum of k primes. We extend the existing result for k=2 to a general k, for which we obtain a better error term. Moreover, we prove an equivalence between the Riemann Hypothesis and a good average order in this case.
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The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function
The paper attempts to prove an equivalence between the error in a smooth weighted prime number theorem and zero-free regions for the Riemann zeta function, but critical proof errors undermine the result.