Farzad Aryan

Let $d(n)=\sum_{d|n} 1$. This is known as the divisor function. It counts the number of divisors of an integer. Consider the following shifted convolution sum \begin{equation*} \sum_{an-m=h}d(n) \, d(m) \, f(an, m), \end{equation*} where $f$ is a...

The Riemann Hypothesis predicts that all zeros of the Riemann zeta function are located on the line Re(s) = 1/2. Also, we have that the number of zeros with imaginary parts located between T and 2T is approximately (T log T)/(2pi). Therefore the...

We discuss the possibility that the Riemann zeta function has a zero s+iT to the left of the classical zero free region. We will show how the existence of this zero forces the function to have many more zeros in the vicinity of s+iT or/and s+2iT.