Sign changes of error terms related to arithmetical functions
Sign changes of error terms related to arithmetical functions
Let H(x)=∑ n≤x φ(n) n-6 π 2 x. Motivated by a conjecture of Erdös, Lau developed a new method and proved that #{n≤T:H(n)H(n+1)<0}≫T. We consider arithmetical functions f(n)=∑ d∣n b d d whose summation can be expressed as ∑ n≤x f(n)=αx+P(log(x))+E(x), where P(x) is a polynomial, E(x)=-∑ n≤y(x) b n …