arXiv subjects
Publications and source records attributed to Irina Rezvyakova.
In 2025, Boaz Klartag proved that there exists a lattice sphere packing in $\mathbb{R}^n$ whose density is at least \[ c n^2 2^{-n}, \] where $c>0$ is an absolute constant. Our aim is to refine the analysis of Klartag's argument and to show that the constant can be taken as \[ c = \frac{1}{2e} - o(1), \qquad n\to\infty. \]
This is an article, published in Izvestiya: Mathematics, 2016, Volume 80, Issue 3, which complements arxiv:2411.18492
We prove for L-function attached to an automorphic cusp form for the Hecke congruence group $Γ_0(D)$, which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical line. This result extends the work of J.L. Hafner of 1983 where the case of the full modular group is considered.
In this paper we consider certain 1-parametric family of Dirichlet series. For a particular value of the parameter the series turns into the Dirichlet series for the Riemann zeta function. We prove that almost every series of the family has analytic continuation to the half plane Re s > 1/2 where it doesn't vanish. The result was obtained before by different authors. We give its simple proof in terms of estimates of some trigonometric sums.