Let Λ (n) be the Von Mangoldt function and rSP (n) = m1+m2 2+m2 3=n Λ (m1) Λ (m2) Λ (m3) be the counting function for the numbers that can be written as sum of a prime and two squares. Let N be a sufficiently large integer. We prove that n≤N rSP (n) (N − n) k Γ (k + 1) = Nk+2π 4Γ (k + 3) + E (N,k) for k > 3/2, where E (N,k) consists of lower order terms that are given in terms of k and sum over the non-trivial zeros of the Riemann zeta function
On the Cesàro average of the numbers that can be written as sum of a prime and two squares of primes
Marco Cantarini
2018
Abstract
Let Λ (n) be the Von Mangoldt function and rSP (n) = m1+m2 2+m2 3=n Λ (m1) Λ (m2) Λ (m3) be the counting function for the numbers that can be written as sum of a prime and two squares. Let N be a sufficiently large integer. We prove that n≤N rSP (n) (N − n) k Γ (k + 1) = Nk+2π 4Γ (k + 3) + E (N,k) for k > 3/2, where E (N,k) consists of lower order terms that are given in terms of k and sum over the non-trivial zeros of the Riemann zeta functionFile in questo prodotto:
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