Bounds of weighted sums of Mangoldt function under the Riemann Hypothesis - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T05:33:20Z http://mathoverflow.net/feeds/question/109973 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109973/bounds-of-weighted-sums-of-mangoldt-function-under-the-riemann-hypothesis Bounds of weighted sums of Mangoldt function under the Riemann Hypothesis Ankush 2012-10-18T03:52:30Z 2012-10-18T07:57:23Z <p>Hello,</p> <p>Can anyone help me with the following implication of the GRH which is fundamental while proving the Odd Goldbach's Conjecture?</p> <p>$$\psi(x,\chi):=\sum_{n\leq x}\Lambda(n)\chi(n)=O(x^{1/2}\log^2 x)$$ where $\chi$ is a non-trivial Dirichlet character.</p> <p>Also tell me the difference in proof while considering the trivial Dirichlet Character, $\chi$.</p> <p>Thank You.</p> http://mathoverflow.net/questions/109973/bounds-of-weighted-sums-of-mangoldt-function-under-the-riemann-hypothesis/109986#109986 Answer by Greg Martin for Bounds of weighted sums of Mangoldt function under the Riemann Hypothesis Greg Martin 2012-10-18T07:57:23Z 2012-10-18T07:57:23Z <p>This can be found, for example, as Theorem 13.7 in Montgomery and Vaughan's <em>Multiplicative Number Theory I. Classical Theory</em>.</p>