Let $\Lambda $ be the von Mangoldt function and $ R (n)\!=\!\sum _ {h+ k= n}\!\Lambda
(h)\Lambda (k) $ be the counting function for the Goldbach numbers. Let $ N\geq 2$ and …

This paper gives an explicit version of Selberg's mean-value estimate for the prime number
theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to …

Sum of one prime and two squares of primes in short intervals - ScienceDirect Skip to main
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Short intervals asymptotic formulae for binary problems with primes and powers, II: density 1
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Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 |
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arXiv:1606.00860v1 [math.NT] 2 Jun 2016 Page 1 arXiv:1606.00860v1 [math.NT] 2 Jun 2016
Riv. Mat. Univ. Parma, Vol. x (2016), 000-000 Alessandro Languasco Applications of some …

Let rv (N) denote the number of representations of the integer N as a sum of v square-free
numbers. We obtain unconditional and conditional bounds for the error term in the …

In this paper, assuming a variant of the Generalized Riemann Hypothesis, which does not
exclude the existence of real zeros, we prove an asymptotic formula for the mean value of …

Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit
formula for the number of representations of an integer as a sum of k⩾ 5 primes. Our error …

In 1973, Montgomery [12] introduced, in order to study the vertical distribution of the zeros of
the Riemann zeta function, the pair correlation functionwhere w (u)= 4/(4+ u2) and γjj= 1, 2 …