Blar i NTNU Open på forfatter "Chirre, Andrés"

Viser treff 1-15 av 15

    • A Conditional Bound for the Riemann zeta-function in the Critical Line 

      Tell, William (Master thesis, 2022)
      Denne oppgaven bestemmer eksplisitte konstanter for den øvre begrensningen av logaritmen til Riemann zeta-funksjonen på den kritiske linja, under antakelsen av Riemann-hypotesen. Dette krever to betraktninger. Vi finner ...

    • A note on entire L-functions 

      Chirre, Andrés (Journal article; Peer reviewed, 2019)
      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 hypothesis. The examples include the entire ...

    • Bounding the log-derivative of the zeta-function 

      Chirre, Andrés; Gonçalves, Felipe (Peer reviewed; Journal article, 2021)
      Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann’s zeta-function in the critical strip.

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

      Chirre, Andrés; Hagen, Markus Valås; Simonič, Aleksander (Peer reviewed; Journal article, 2023)

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

      Chirre, Andrés (Journal article; Peer reviewed, 2019)
      Let S(σ, t) =1πargζ(σ+it)be the argument of the Riemann zeta function at the point σ+itof the critical strip. Fo r n ≥1and t >0we defineSn(σ, t)=t∫0Sn−1(σ, τ)dτ+δn,σ,where δn,σis a specific constant depending on σand n. ...

    • Fourier optimization and quadratic forms 

      Chirre, Andrés; Quesada-Herrera, Oscar (Peer reviewed; Journal article, 2021)
      We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer ℓ≥1⁠, we improve the error term in the partial sums of the number ...

    • Large oscillations of the argument of the Riemann zeta-function 

      Chirre, Andrés; Mahatab, Kamalakshya (Journal article; Peer reviewed, 2021)

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

      Chirre, Andrés; Mahatab, Kamalakshya (Journal article; Peer reviewed, 2021)

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

      Chirre, Andrés (Peer reviewed; Journal article, 2022)
      Assuming the Riemann hypothesis, we obtain a formula for the mean value of the -derivative of , depending on the pair correlation of zeros of the Riemann zeta-function. This formula allows us to obtain new equivalences ...

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

      Chirre, Andrés; Velásquez, Oswaldo (Peer reviewed; Journal article, 2020)
      In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ-function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach ...

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

      Carneiro, Emanuel; Chandee, Vorrapan; Chirre, Andrés; Milinovich, Micah B. (Peer reviewed; Journal article, 2022)
      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 intervals, the second is an integral introduced by ...

    • Optimality for the two-parameter quadratic sieve 

      Carneiro, Emanuel; Helfgott, Harald Andrés; Chirre, Andrés; Mejía-Cordero, Julián (Peer reviewed; Journal article, 2022)
      We study the two-parameter quadratic sieve for an arbitrary smoothing function. We prove, under some very general assumptions, that the function considered by Barban and Vekhov (1968) and Graham (1978) for this problem is ...

    • Pair Correlation estimates for the zeros of the zeta function via semidefinite programming 

      Chirre, Andrés; Gonçalves, Felipe; De Laat, David (Peer reviewed; Journal article, 2020)
      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 semidefinite programming to improve upon ...

    • Primes In Arithmetic Progressions And Semidefinite Programming 

      Chirre, Andrés; Júnior, Valdir José Pereira; de Laat, David (Journal article; Peer reviewed, 2021)
      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 by Carneiro, Milinovich and Soundararajan ...

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

      Chirre, Andrés; Quesada-Herrera, Oscar (Journal article; Peer reviewed, 2021)