7 papers
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.
Large values of the argument of the Riemann zeta-function and its iterates
Andrés Chirre, Kamalakshya Mahatab
Let be the argument of the Riemann zeta-function at the point in the critical strip. For and , we define \begin{equation*} S_{n}…
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…
A note on the zeros of approximations of the Ramanujan 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 function given by Haseo Ki, and we provide a new proof of his re…
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 (and other L-functions) using Montgomery's pair correlation approach. We use se…
Extreme values for near the critical line
Andrés Chirre
Let be the argument of the Riemann zeta function at the point of the critical strip. For and we define $$ S_{n}(σ,t) = \int_0^t…