6 citations · 10 across the 6 of their papers we have counts for
8 papers
On the Imaginary Part of
Farzad Aryan
We derive an explicit zero-side formula for the imaginary part of a smooth truncation of the logarithmic derivative of the Riemann zeta-function. The resulting kernel is the odd co…
Pair Correlation Factor and the Sample Complexity of Gaussian Mixtures
Farzad Aryan
We study the problem of learning Gaussian Mixture Models (GMMs) and ask: which structural properties govern their sample complexity? Prior work has largely tied this complexity to…
Higher moments of distribution of zeta zeros
Farzad Aryan
We develop a method for mean-value estimation of long Dirichlet polynomials. For an application, we use our method to study properties of the logarithmic derivative of the Riemann…
A new approach to gaps between zeta zeros
Farzad Aryan
We study the value-distribution of Dirichlet polynomials on the critical line . As a consequence, we prove a corollary on small consecutive gaps between zeros…
On an extension of the Landau-Gonek formula
Farzad Aryan
We prove an extension of the Landau-Gonek formula. As an application we recover unconditionally some of the consequences of a pair correlation estimate that previously was known un…
On binary and quadratic divisor problems
Farzad Aryan
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
Distribution of squares modulo a composite number
Farzad Aryan
In this paper we study the distribution of squares modulo a square-free number . We also look at inverse questions for the large sieve in the distribution aspect and we make imp…
The distribution of -tuples of reduced residues
Farzad Aryan
In 1940 Paul Erdős made a conjecture about the distribution of reduced residues. Here we study the distribution of -tuple of reduced residues.