A. Bondarenko

activity

20032026

most citedLarge GCD sums and extreme values of the Riemann zeta function

50 citations · 236 across the 25 of their papers we have counts for

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11 papers · 1 filter

math.NT2023★ 2 cited

A dichotomy for extreme values of zeta and Dirichlet L-functions

Andriy Bondarenko, Pranendu Darbar, Markus Valås Hagen +2

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maxi…

math.NT2020★ 1 cited

Fourier interpolation with zeros of zeta and $L$ -functions

Andriy Bondarenko, Danylo Radchenko, Kristian Seip

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the…

math.NT2018

On certain sums over ordinates of zeta-zeros II

Andriy Bondarenko, Aleksandar Ivić, Eero Saksman +1

Let $γ$ denote the imaginary parts of complex zeros $ρ = β + iγ$ of $ζ (s)$ . The problem of analytic continuation of the function $G (s) := γ > 0 \sum γ^{- s}$ to the left of the…

math.NT2017★ 43 cited

Extreme values of the Riemann zeta function and its argument

Andriy Bondarenko, Kristian Seip

We combine our version of the resonance method with certain convolution formulas for $ζ (s)$ and $lo g ζ (s)$ . This leads to a new $Ω$ result for $∣ ζ (1/2 + i t) ∣$ : The maximum of $|ζ(…

math.NT2017

Note on the resonance method for the Riemann zeta function

Andriy Bondarenko, Kristian Seip

We improve Montgomery's $Ω$ -results for $∣ ζ (σ + i t) ∣$ in the strip $1/2 < σ < 1$ and give in particular lower bounds for the maximum of $∣ ζ (σ + i t) ∣$ on $T \leq t \leq T$ that are unif…

math.NT2015★ 8 cited

Gál-type GCD sums beyond the critical line

Andriy Bondarenko, Titus Hilberdink, Kristian Seip

We prove that \[ \sum_{k,{\ell}=1}^N\frac{(n_k,n_{\ell})^{2α}}{(n_k n_{\ell})^α} \ll N^{2-2α} (\log N)^{b(α)} \] holds for arbitrary integers $1 \leq n_{1} < \dots < n_{N}$ and $0 < α < 1/2$ …

math.NT2015★ 50 cited

Large GCD sums and extreme values of the Riemann zeta function

Andriy Bondarenko, Kristian Seip

It is shown that the maximum of $∣ ζ (1/2 + i t) ∣$ on the interval $T^{1/2} \leq t \leq T$ is at least $exp ((1/ 2 + o (1)) lo g T lo g lo g lo g T / lo g lo g T)$ . Our pro…

math.NT2014★ 23 cited

Helson's problem for sums of a random multiplicative function

Andriy Bondarenko, Kristian Seip

We consider the random functions $S_{N} (z) := \sum_{n = 1}^{N} z (n)$ , where $z (n)$ is the completely multiplicative random function generated by independent Steinhaus variables $z (p)$ . It…

math.NT2014★ 26 cited

An inequality of Hardy--Littlewood type for Dirichlet polynomials

Andriy Bondarenko, Winston Heap, Kristian Seip

The $L^{q}$ norm of a Dirichlet polynomial $F (s) = \sum_{n = 1}^{N} a_{n} n^{- s}$ is defined as \[\| F\|_q:=(\lim_{T\to\infty}\frac{1}{T}\int_{0}^T |F(it)|^qdt)^{1/q}\] for $0 < q < \infty$ . I…

math.NT2014★ 22 cited

GCD sums and complete sets of square-free numbers

Andriy Bondarenko, Kristian Seip

It is proved that \[ \sum_{k,{\ell}=1}^N\frac{\gcd(n_k,n_{\ell})}{\sqrt{n_k n_{\ell}}} \ll N\exp\left(C\sqrt{\frac{\log N \log\log\log N}{\log\log N}}\right) \] holds for arbitrary…

math.NT2003★ 5 cited

On certain sums over ordinates of zeta zeros

Aleksandar Ivić

Let $γ$ denote imaginary parts of complex zeros of the Riemann zeta-function $ζ (s)$ . Certain sums over the $γ$ 's are evaluated, by using the function $G (s) = \sum_{γ > 0} γ^{- s}$ and…

A dichotomy for extreme values of zeta and Dirichlet L-functions

Fourier interpolation with zeros of zeta and L-functions

On certain sums over ordinates of zeta-zeros II

Extreme values of the Riemann zeta function and its argument

Note on the resonance method for the Riemann zeta function

Gál-type GCD sums beyond the critical line

Large GCD sums and extreme values of the Riemann zeta function

Helson's problem for sums of a random multiplicative function

An inequality of Hardy--Littlewood type for Dirichlet polynomials

GCD sums and complete sets of square-free numbers

On certain sums over ordinates of zeta zeros

Fourier interpolation with zeros of zeta and $L$ -functions