Euler phi fonksiyonu ve bölme fonksiyonunun ortalama değerindeki işaret değişimleri

In this study, we analyze the error terms in average orders of Euler phi function and divisor function. Our aim is to obtain a omega type estimation for these error terms and show that they change sign infinitely often. In the first part, we find the average value of the error term in the average order of Euler phi function and obtain a omega type estimation for this error term by employing basic arguments in Number Theory. In the second part, we show that this error term changes sign infinitely often. We accomplish this result by averaging this error term over arithmetic progressions. In the third part we utilize complicated methods to improve the results that we found in the first two parts. Finally, we combine the methods we used up to this section and apply them to the divisor function which is defined to be the sum of divisors of a given number n which is relatively prime to a.