8 papers
Almost all of the zeros of the Riemann zeta-function are on the critical line
Tatyana Preobrazhenskaya, Sergei Preobrazhenskii
This is a reworked version of the paper. An idea that allows us to circumvent limitations of previous approaches is not to apply arithmetic-geometric mean inequality and the second…
A small improvement in the small gaps between consecutive zeros of the Riemann zeta-function
Sergei Preobrazhenskii
Feng and Wu introduced a new general coefficient sequence into Montgomery and Odlyzko's method for exhibiting irregularity in the gaps between consecutive zeros of assuming…
A note on correlations of arithmetic functions
Sergei Preobrazhenskii, Tatyana Preobrazhenskaya
In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem wh…
On a choice of the mollified function in the Levinson-Conrey method
Sergei Preobrazhenskii, Tatyana Preobrazhenskaya
Motivated by a functional property of the Riemann zeta function, we consider a new form of the mollified function in the Levinson-Conrey method. As an application, we give the foll…
A general inversion formula for summatory arithmetic functions and its application to the summatory function of the Moebius function
Sergei Preobrazhenskii
We prove an inversion formula for summatory arithmetic functions. As an application, we obtain an arithmetic relationship between summatory Piltz divisor functions and a sum of the…
An analogue of Selberg's formula for Motohashi's product
Sergei Preobrazhenskii
We prove an analogue of Selberg's explicit formula for Motohashi's product (see arXiv:1104.1358v3 [math.NT]). We also provide a zero-density theorem for the product, which follows…