Andrés Chirre

collaborators

4 papers

math.NT2026

Explicit conditional bounds for $I^¶ (s)$ at the edge of the critical strip

AndrÃ©s 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

AndrÃ©s Chirre, Markus ValÃ¥s 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

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

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…

Explicit conditional bounds for I^¶(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

Explicit conditional bounds for $I^¶ (s)$ at the edge of the critical strip