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

Showing 2020Show all

6 papers · 1 filter

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…

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

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

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