3 papers
math.GM2018
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…
math.NT2014
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…
math.NT2014
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…