Andrés Chirre

activity

20172026

most citedBandlimited approximations and estimates for the Riemann zeta-function

16 citations · 46 across the 17 of their papers we have counts for

collaborators

25 papers

math.NT2026

Explicit conditional bounds for $ζ (s)$ at the edge of the critical strip

Andrés Chirre, Blas Molero Ravines

In this paper, we obtain explicit bounds for the real part of the logarithmic derivative of the Riemann zeta-function on the line $\re s=1$, assuming the Riemann hypothesis. The pr…

math.NT2025

On Goldbach numbers in short intervals

Andrés Chirre, Markus Valås Hagen

Assuming the Riemann Hypothesis, we prove that for all $x \geq 2$ , there exists at least one even integer within the interval $(x, x + 123 lo g^{2} x]$ , that can be expressed as the sum o…

math.NT2025

Optimal bounds for sums of non-negative arithmetic functions

Andrés Chirre, Harald Andrés Helfgott

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series admitting meromorphic continuation to the complex plane. Assume we know the location of the poles of $A (s)$ with $|\Im s| \leq…

math.NT2025

Optimal bounds for sums of bounded arithmetic functions

Andrés Chirre, Harald Andrés Helfgott

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series with meromorphic continuation. Say we are given information on the poles of $A (s)$ with $∣ℑ s ∣ \leq T$ for some large constan…

math.NT2023

Bounding zeta on the 1-line under the partial Riemann hypothesis

Andrés Chirre

We provide explicit bounds in the theory of the Riemann zeta-function at the line $ℜ s = 1$ , assuming that the Riemann hypothesis holds until the height $T$ . In particular, we imp…

math.NT2023

Remarks on a Formula of Ramanujan

Andrés Chirre, Steven M. Gonek

Assuming an averaged form of Mertens' conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyz…

math.CA2023

An extremal problem and inequalities for entire functions of exponential type

Andrés Chirre, Dimitar K. Dimitrov, Emily Quesada-Herrera +1

We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carathéodory--Fejér--Turán problem. The first variation impos…

math.CA2022★ 5 cited

Point evaluation in Paley--Wiener spaces

Ole Fredrik Brevig, Andrés Chirre, Joaquim Ortega-Cerdà +1

We study the norm of point evaluation at the origin in the Paley--Wiener space $P W^{p}$ for $0 < p < \infty$ , i. e., we search for the smallest positive constant $C$ , called $\mathsc…

math.NT2022★ 6 cited

Conditional estimates for the logarithmic derivative of Dirichlet $L$ -functions

Andrés Chirre, Aleksander Simonič, Markus Valås Hagen

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$ -aspect for the logarithmic derivative $(L^{'} / L) (σ, χ)$ of Dirichlet $L$ -func…

math.NT2021

Hilbert spaces and low-lying zeros of L-functions

Emanuel Carneiro, Andrés Chirre, Micah B. Milinovich

Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$ -functions in a…

math.NT2021★ 6 cited

On Montgomery's pair correlation conjecture: a tale of three integrals

Emanuel Carneiro, Vorrapan Chandee, Andrés Chirre +1

We study three integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. The first is the integral of Montgomery's function $F (α, T)$ in bounded interval…

math.NT2021

A note on the mean values of the derivatives of $ζ^{'} / ζ$

Andrés Chirre

Assuming the Riemann hypothesis, we obtain a formula for the mean value of the $k$ -derivative of $ζ^{'} / ζ$ , depending on the pair correlation of zeros of the Riemann zeta-function. Th…

math.NT2021

Bounding the log-derivative of the zeta-function

Andrés Chirre, Felipe Gonçalves

Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann's zeta-function in the critical strip.

math.NT2020

Fourier optimization and quadratic forms

Andrés Chirre, Emily Quesada-Herrera

We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $ℓ \geq 1$ , we improve…

math.NT2020

The second moment of $S_{n} (t)$ on the Riemann hypothesis

Andrés Chirre, Emily Quesada-Herrera

Let $S (t) = \frac{1}{π} ar g ζ (1/2 + i t)$ be the argument of the Riemann zeta-function at the point $\frac{1}{2} + i t$ . For $n \geq 1$ and $t > 0$ define its antiderivatives a…

math.NT2020

Large values of the argument of the Riemann zeta-function and its iterates

Andrés Chirre, Kamalakshya Mahatab

Let $S (σ, t) = \frac{1}{π} ar g ζ (σ + i t)$ be the argument of the Riemann zeta-function at the point $σ + i t$ in the critical strip. For $n \geq 1$ and $t > 0$ , we define \begin{equation*} S_{n}…

math.NT2020

Optimality for the two-parameter quadratic sieve

Emanuel Carneiro, Andrés Chirre, Harald Andrés Helfgott +1

We study the two-parameter quadratic sieve for a general test function. We prove, under some very general assumptions, that the function considered by Barban and Vehov [BV68] and G…

math.NT2020

Primes in arithmetic progressions and semidefinite programming

Andrés Chirre, Valdir José Pereira Júnior, David de Laat

Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed…

math.NT2020

A note on the zeros of approximations of the Ramanujan $Ξ -$ function

Andrés Chirre, Oswaldo Velásquez Castañón

In this paper, we review the study of the distribution of the zeros of certain approximations for the Ramanujan $Ξ -$ function given by Haseo Ki, and we provide a new proof of his re…

math.NT2019

Large Oscillations of the Argument of the Riemann Zeta-function

Andrés Chirre, Kamalakshya Mahatab

Let $S (t)$ denote the argument of the Riemann zeta-function, defined as $S (t) = \frac{1}{π} ℑ lo g ζ (1/2 + i t) .$ Assuming the Riemann hypothesis, we prove that $$ S(t)=Ω_{\pm}\bigg…

math.NT2018

Pair Correlation Estimates for the Zeros of the Zeta Function via Semidefinite Programming

Andrés Chirre, Felipe Gonçalves, David de Laat

In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function $ζ (s)$ (and other L-functions) using Montgomery's pair correlation approach. We use se…

math.NT2018

Extreme values for $S_{n} (σ, t)$ near the critical line

Andrés Chirre

Let $S (σ, t) = \frac{1}{π} ar g ζ (σ + i t)$ be the argument of the Riemann zeta function at the point $σ + i t$ of the critical strip. For $n \geq 1$ and $t > 0$ we define $$ S_{n}(σ,t) = \int_0^t…

math.NT2018

A note on entire $L$ -functions

Andrés Chirre

In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$ -functions in the critical strip, under the generalized Riemann hypot…

math.NT2017★ 16 cited

Bandlimited approximations and estimates for the Riemann zeta-function

Emanuel Carneiro, Andrés Chirre, Micah B. Milinovich

In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Ri…

Explicit conditional bounds for ζ(s) at the edge of the critical strip

On Goldbach numbers in short intervals

Optimal bounds for sums of non-negative arithmetic functions

Optimal bounds for sums of bounded arithmetic functions

Bounding zeta on the 1-line under the partial Riemann hypothesis

Remarks on a Formula of Ramanujan

An extremal problem and inequalities for entire functions of exponential type

Point evaluation in Paley--Wiener spaces

Conditional estimates for the logarithmic derivative of Dirichlet L-functions

Hilbert spaces and low-lying zeros of L-functions

On Montgomery's pair correlation conjecture: a tale of three integrals

A note on the mean values of the derivatives of ζ′/ζ

Bounding the log-derivative of the zeta-function

Fourier optimization and quadratic forms

The second moment of Sn​(t) on the Riemann hypothesis

Large values of the argument of the Riemann zeta-function and its iterates

Optimality for the two-parameter quadratic sieve

Primes in arithmetic progressions and semidefinite programming

A note on the zeros of approximations of the Ramanujan Ξ−function

Large Oscillations of the Argument of the Riemann Zeta-function

Pair Correlation Estimates for the Zeros of the Zeta Function via Semidefinite Programming

Extreme values for Sn​(σ,t) near the critical line

A note on entire L-functions

Bandlimited approximations and estimates for the Riemann zeta-function

Explicit conditional bounds for $ζ (s)$ at the edge of the critical strip

Conditional estimates for the logarithmic derivative of Dirichlet $L$ -functions

A note on the mean values of the derivatives of $ζ^{'} / ζ$

The second moment of $S_{n} (t)$ on the Riemann hypothesis

A note on the zeros of approximations of the Ramanujan $Ξ -$ function

Extreme values for $S_{n} (σ, t)$ near the critical line

A note on entire $L$ -functions