On the Cesaro average of the numbers that can be written as sum of a prime and two squares of primes

作者：Cantarini Marco^*

来源：Journal of Number Theory, 2018, 185: 194-217.

DOI：10.1016/j.jnt.2017.09.001

• Goldbach-type theorems
• Laplace transforms
• Cesaro average

Let A (n) be the Von Mangoldt function and r(SP) (n) = Sigma(m1)+m(2)(2)+m(2/3=n) Lambda(m(1)) Lambda (m(2)) Lambda (m(3)) 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
Sigma(n <= N) r(SP) (n) (N-n)(k)/Gamma(k+1) = Nk+2 pi/4 Gamma(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.

• 出版日期2018-4