On the Mean Value of Arithmetic Error Terms

In the 1980’s author proved lower bounds for mean value of modulus error term prime number theorem and other important theoretic functions whose oscillation is in connection with zeros Riemann zeta function. present work a general shown simple way which gives bound mentioned as function hypothetical pole Mellin transform The conditions are amply satisfied such results recover earlier ones (even slightly sharper form). obtained estimates often optimal apart from constant factor, at least under reasonable Hypothesis. This case, particular, theorem.