R. Garunkštis

activity

20102026

most citedNotes on Universality in Short Intervals and Exponential Shifts

15 citations · 27 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2026

The discrete second moment of the Riemann zeta-function along powers of Gram points

Marius Dundulis, Ramūnas Garunkštis, Antanas Laurinčikas +1

Let $t_{k}$ be the Gram points, and let $d \geq 1$ be a fixed integer. Put $η_{d} = 1/ (2^{d + 1} - 2)$ , $σ_{d} = 1 - η_{d} / d$ , and $σ_{d}^{*} = 7/8$ for $d = 2$ and $σ_{d}^{*} = σ_{d}$ otherwise. We prove that, unifo…

math.NT2026

Higher derivatives of the Gram function

Marius Dundulis, Ramūnas Garunkštis, Antanas Laurinčikas +1

We study the nonlinear phenomenon of the asymptotics of higher-order derivatives of the Gram function $t_{u}$ . We also prove the uniform distribution and continuous uniform distribut…

math.NT2025

Second moments of general Dirichlet series and Selberg zeta functions at $σ = 1$

Ramūnas Garunkštis, Jokūbas Putrius

In this paper, we prove the existence of the second moment at $σ = 1$ for a general Dirichlet series with positive coefficients whose partial sum of the coefficients up to $x$ satisf…

math.NT2025

The Lindelöf Hypothesis for Zeta Zero Ordinates

Ramūnas Garunkštis, Athanasios Sourmelidis, Jörn Steuding

We provide conditional and unconditional asymptotic formulae for the exponential sums $\sum_{γ} γ^{- i τ}$ , where the summation is over the ordinates of the nontrivial zeros $ρ = β + iγ$ …

math.NT2023★ 15 cited

Notes on Universality in Short Intervals and Exponential Shifts

Johan Andersson, Ramūnas Garunkštis, Roma Kačinskaitė +6

We improve a recent universality theorem for the Riemann zeta-function in short intervals due to Antanas Laurinčikas with respect to the length of these intervals. Moreover, we pro…

math.NT2019

Symmetry of zeros of Lerch zeta-function for equal parameters

Ramūnas Garunkštis, Rokas Tamošiūnas

For most values of parameters $λ$ and $α$ , the zeros of the Lerch zeta-function $L (λ, α, s)$ are distributed very chaotically. In this paper we consider the special case of equal p…

math.NT2010★ 12 cited

On the roots of the equation $ζ (s) = a$

R. Garunkstis, J. Steuding

Given any complex number $a$ , we prove that there are infinitely many simple roots of the equation $ζ (s) = a$ with arbitrarily large imaginary part. Besides, we give a heuristic inte…

math.NT2010

Self-approximation of Dirichlet L-functions

R. Garunkstis

Let $d$ be a real number, let $s$ be in a fixed compact set of the strip $1/2 < σ < 1$ , and let $L (s, χ)$ be the Dirichlet $L$ -function. The hypothesis is that for any real number $d$ …